survey

A Survey on the Densest Subgraph Problem and its Variants

Authors:

Tommaso Lanciano,

Atsushi Miyauchi,

Adriano Fazzone,

Francesco BonchiAuthors Info & Claims

ACM Computing Surveys, Volume 56, Issue 8

Article No.: 208, Pages 1 - 40

https://doi.org/10.1145/3653298

Published: 30 April 2024 Publication History

Abstract

The Densest Subgraph Problem requires us to find, in a given graph, a subset of vertices whose induced subgraph maximizes a measure of density. The problem has received a great deal of attention in the algorithmic literature since the early 1970s, with many variants proposed and many applications built on top of this basic definition. Recent years have witnessed a revival of research interest in this problem with several important contributions, including some groundbreaking results, published in 2022 and 2023. This survey provides a deep overview of the fundamental results and an exhaustive coverage of the many variants proposed in the literature, with a special attention to the most recent results. The survey also presents a comprehensive overview of applications and discusses some interesting open problems for this evergreen research topic.

References

[1]

S. Ahmadian and S. Haddadan. 2021. The wedge picking model: A theoretical analysis of graph evolution caused by triadic closure and algorithmic implications. J. Strateg. Innov. Sust. 16, 3 (2021), 74–93.

[2]

A. Anagnostopoulos, L. Becchetti, A. Fazzone, C. Menghini, and C. Schwiegelshohn. 2020. Spectral relaxations and fair densest subgraphs. In Proceedings of the 29th ACM International Conference on Information and Knowledge Management (CIKM’20). 35–44.

Digital Library

[3]

R. Andersen and K. Chellapilla. 2009. Finding dense subgraphs with size bounds. In Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph (WAW’09). 25–37.

Digital Library

[4]

A. Angel, N. Sarkas, N. Koudas, and D. Srivastava. 2012. Dense subgraph maintenance under streaming edge weight updates for real-time story identification. Proc. VLDB Endow. 5, 6 (2012), 574–585.

Digital Library

[5]

S. Arora, E. Hazan, and S. Kale. 2012. The multiplicative weights update method: A meta-algorithm and applications. Theory Comput. 8, 1 (2012), 121–164.

[6]

S. Arora, D. Karger, and M. Karpinski. 1995. Polynomial time approximation schemes for dense instances of NP-hard problems. In Proceedings of the 27th Annual ACM Symposium on Theory of Computing (STOC’95). 284–293.

Digital Library

[7]

J. M. Arrazola and T. R. Bromley. 2018. Using gaussian boson sampling to find dense subgraphs. Phys. Rev. Lett. 121, 3 (2018), 030503.

[8]

Y. Asahiro, K. Iwama, H. Tamaki, and T. Tokuyama. 2000. Greedily finding a dense subgraph. J. Algor. 34, 2 (2000), 203–221.

Digital Library

[9]

J. Backer and J. M. Keil. 2010. Constant factor approximation algorithms for the densest k-subgraph problem on proper interval graphs and bipartite permutation graphs. Inform. Process. Lett. 110, 16 (2010), 635–638.

Digital Library

[10]

B. Bahmani, A. Goel, and K. Munagala. 2014. Efficient primal-dual graph algorithms for MapReduce. In Proceedings of the 11th International Workshop on Algorithms and Models for the Web-Graph (WAW). Springer, 59–78.

Digital Library

[11]

B. Bahmani, R. Kumar, and S. Vassilvitskii. 2012. Densest subgraph in streaming and MapReduce. Proc. VLDB Endow. 5, 5 (2012), 454–465.

Digital Library

[12]

O. D. Balalau, F. Bonchi, T. H. H. Chan, F. Gullo, and M. Sozio. 2015. Finding subgraphs with maximum total density and limited overlap. In Proceedings of the 8th ACM International Conference on Web Search and Data Mining (WSDM’15). 379–388.

Digital Library

[13]

S. Barman. 2018. Approximating Nash equilibria and dense subgraphs via an approximate version of Carathéodory’s theorem. SIAM J. Comput. 47, 3 (2018), 960–981.

Digital Library

[14]

S. K. Bera, S. Bhattacharya, J. Choudhari, and P. Ghosh. 2022. A new dynamic algorithm for densest subhypergraphs. In Proceedings of the ACM Web Conference (TheWebConf’22). 1093–1103.

Digital Library

[15]

T. Bhadra and S. Bandyopadhyay. 2021. Supervised feature selection using integration of densest subgraph finding with floating forward–backward search. Inf. Sci. 566 (2021), 1–18.

Digital Library

[16]

A. Bhaskara, M. Charikar, E. Chlamtac, U. Feige, and A. Vijayaraghavan. 2010. Detecting high log-densities: An \({O}(n^{1/4})\) approximation for densest k-Subgraph. In Proceedings of the 42nd ACM Symposium on Theory of Computing (STOC’10). 201–210.

Digital Library

[17]

A. Bhaskara, M. Charikar, V. Guruswami, A. Vijayaraghavan, and Y. Zhou. 2012. Polynomial integrality gaps for strong SDP relaxations of Densest k-subgraph. In Proceedings of the 23rd Annual ACM–SIAM Symposium on Discrete Algorithms (SODA’12). 388–405.

[18]

S. Bhattacharya, M. Henzinger, D. Nanongkai, and C.E. Tsourakakis. 2015. Space- and time-efficient algorithm for maintaining dense subgraphs on one-pass dynamic streams. In Proceedings of the 47th Annual ACM Symposium on Theory of Computing (STOC’15). 173–182.

Digital Library

[19]

A. Billionnet, S. Elloumi, and M.C. Plateau. 2009. Improving the performance of standard solvers for quadratic 0-1 programs by a tight convex reformulation: The QCR method. Discr. Appl. Math. 157, 6 (2009), 1185–1197.

Digital Library

[20]

S. Böcker and J. Baumbach. 2013. Cluster editing. In The Nature of Computation. Logic, Algorithms, Applications, P. Bonizzoni, V. Brattka, and B. Löwe (Eds.). 33–44.

[21]

P. Bogdanov, M. Mongiovì, and A.K. Singh. 2011. Mining heavy subgraphs in time-evolving networks. In Proceedings of the 11th IEEE International Conference on Data Mining (ICDM’11). 81–90.

Digital Library

[22]

V. Boginski, S. Butenko, and P. Pardalos. 2003. On structural properties of the market graph. Innov. Financ. Econ. Netw. 48 (2003), 29–35.

[23]

P. Bombina and B. Ames. 2020. Convex optimization for the densest subgraph and densest submatrix problems. SN Operat. Res. Forum 1 (2020), 1–24.

[24]

F. Bonchi, I. Bordino, F. Gullo, and G. Stilo. 2016. Identifying buzzing stories via anomalous temporal subgraph discovery. In Proceedings of the IEEE/WIC/ACM International Conference on Web Intelligence (WI’16). 161–168.

[25]

F. Bonchi, I. Bordino, F. Gullo, and G. Stilo. 2019. The importance of unexpectedness: Discovering buzzing stories in anomalous temporal graphs. Web Intell. 17, 3 (2019), 177–198.

[26]

F. Bonchi, D. García-Soriano, and F. Gullo. 2022. Correlation clustering. Synth. Lect. Data Min. Knowl. Discov. 12, 1 (Mar.2022), 1–149.

[27]

F. Bonchi, D. García-Soriano, A. Miyauchi, and C.E. Tsourakakis. 2021. Finding densest k-connected subgraphs. Discr. Appl. Math. 305 (2021), 34–47.

Digital Library

[28]

F. Bonchi, F. Gullo, A. Kaltenbrunner, and Y. Volkovich. 2014. Core decomposition of uncertain graphs. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’14). 1316–1325.

Digital Library

[29]

F. Bonchi, A. Khan, and L. Severini. 2019. Distance-generalized core decomposition. In Proceedings of the International Conference on Management of Data (SIGMOD’19). 1006–1023.

Digital Library

[30]

D. Boob, Y. Gao, R. Peng, S. Sawlani, C.E. Tsourakakis, D. Wang, and J. Wang. 2020. Flowless: Extracting densest subgraphs without flow computations. In Proceedings of the ACM Web Conference (TheWebConf’20). 573–583.

Digital Library

[31]

D. Boob, S. Sawlani, and D. Wang. 2019. Faster width-dependent algorithm for mixed packing and covering LPs. In Proceedings of the 33rd Conference on Neural Information Processing Systems (NeurIPS’19). 15253–15262.

[32]

N. Bourgeois, A. Giannakos, G. Lucarelli, I. Milis, and V. T. Paschos. 2013. Exact and approximation algorithms for densest k-Subgraph. In Proceedings of the 7th International Workshop on Algorithms and Computation (WALCOM’13). 114–125.

[33]

M. Braverman, Y.K. Ko, A. Rubinstein, and O. Weinstein. 2017. ETH hardness for densest-k-subgraph with perfect completeness. In Proceedings of the 28th Annual ACM–SIAM Symposium on Discrete Algorithms (SODA’17). 1326–1341.

[34]

H. Broersma, P. A. Golovach, and V. Patel. 2013. Tight complexity bounds for FPT subgraph problems parameterized by the clique-width. Theor. Comput. Sci. 485 (2013), 69–84.

[35]

A. Buluç, H. Meyerhenke, I. Safro, P. Sanders, and C. Schulz. 2016. Recent advances in graph partitioning. In Algorithm Engineering, L. Kliemann and P. Sanders (Eds.). Springer, 117–158.

[36]

J. Cadena, A. Kumar Vullikanti, and Charu C. A.2016. On dense subgraphs in signed network streams. In Proceedings of the 16th IEEE International Conference on Data Mining (ICDM’16). 51–60.

[37]

L. Cai. 2008. Parameterized complexity of cardinality constrained optimization problems. Comput. J. 51, 1 (2008), 102–121.

Digital Library

[38]

L. Chang and L. Qin. 2018. Cohesive Subgraph Computation over Large Sparse Graphs: Algorithms, Data Structures, and Programming Techniques. Springer.

Digital Library

[39]

S. C. Chang, L. H. Chen, L. J. Hung, S. S. Kao, and R. Klasing. 2020. The hardness and approximation of the densest k-subgraph problem in parameterized metric graphs. In Proceedings of the International Computer Symposium (ICS’20). 126–130.

[40]

M. Charikar. 2000. Greedy approximation algorithms for finding dense components in a graph. In Proceedings of the 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX’00). 84–95.

[41]

M. Charikar, Y. Naamad, and J. Wu. 2018. On finding dense common subgraphs. CoRR abs/1802.06361.

[42]

C. Chekuri and K. Quanrud. 2022. (1-\(\epsilon\))-approximate fully dynamic densest subgraph: Linear space and faster update time. CoRR abs/2210.02611.

[43]

C. Chekuri, K. Quanrud, and M. R. Torres. 2022. Densest subgraph: Supermodularity, iterative peeling, and flow. In Proceedings of the 2022 ACM-SIAM Symposium on Discrete Algorithms (SODA’22). SIAM, 1531–1555.

[44]

C. Chekuri and M. R. Torres. 2023. On the generalized mean densest subgraph problem: Complexity and algorithms. arXiv:2306.02172. Retrieved from https://arxiv.org/abs/2306.02172

[45]

D. Z. Chen, R. Fleischer, and J. Li. 2010. Densest k-subgraph approximation on intersection graphs. In Proceedings of the 8th International Workshop on Approximation and Online Algorithms (WAOA’10). 83–93.

[46]

J. Chen and Y. Saad. 2012. Dense subgraph extraction with application to community detection. IEEE Trans. Knowl. Data Eng. 24, 7 (2012), 1216–1230.

Digital Library

[47]

S. Chen, T. Lin, I. King, M. R. Lyu, and W. Chen. 2014. Combinatorial pure exploration of multi-armed bandits. In Proceedings of the 28th Conference on Neural Information Processing Systems (NIPS’14). 379–387.

[48]

T. Chen, F. Bonchi, D. García-Soriano, A. Miyauchi, and C.E. Tsourakakis. 2022. Dense and well-connected subgraph detection in dual networks. In Proceedings of the SIAM International Conference on Data Mining (SDM’22). 361–369.

[49]

T. Chen, B. Matejek, M. Mitzenmacher, and C.E. Tsourakakis. 2022. Algorithmic tools for understanding the motif structure of networks. In Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD’22).

[50]

T. Chen and C. E. Tsourakakis. 2022. Antibenford subgraphs: Unsupervised anomaly detection in financial networks. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD’22). 2762–2770.

Digital Library

[51]

W. Chen, Y. Wang, and Y. Yuan. 2013. Combinatorial multi-armed bandit: General framework and applications. In Proceedings of the 30th International Conference on Machine Learning (ICML’13). 151–159.

[52]

J. Cheriyan, T. Hagerup, and K. Mehlhorn. 1996. An \(o(n^3)\)-time maximum-flow algorithm. SIAM J. Comput. 25, 6 (1996), 1144–1170.

Digital Library

[53]

E. J. Chesler and M. A. Langston. 2005. Combinatorial genetic regulatory network analysis tools for high throughput transcriptomic data. In Proceedings of the Joint Annual RECOMB Satellite Workshops on Systems Biology and on Regulatory Genomics. 150–165.

[54]

E. Chlamtác, M. Dinitz, C. Konrad, G. Kortsarz, and G. Rabanca. 2018. The densest k-subhypergraph problem. SIAM J. Discr. Math. 32, 2 (2018), 1458–1477.

Digital Library

[55]

C. Chekuri, A. B. Christiansen, J. Holm, I. van der Hoog, K. Quanrud, E. Rotenberg, C. Schwiegelshohn. 2024. Adaptive out-orientations with applications. In Proceedings of the 2024 Annual ACM–SIAM Symposium on Discrete Algorithms (SODA’24). 3062–3088.

[56]

D. Chu, F. Zhang, W. Zhang, X. Lin, and Y. Zhang. 2022. Hierarchical core decomposition in parallel: From construction to subgraph search. In Proceedings of the 38th IEEE International Conference on Data Engineering (ICDE’22). 1138–1151.

[57]

L. Chu, Y. Zhang, Y. Yang, L. Wang, and J. Pei. 2019. Online density bursting subgraph detection from temporal graphs. Proc. VLDB Endow. 12, 13 (2019), 2353–2365.

Digital Library

[58]

J. Chuzhoy, M. Dalirrooyfard, V. Grinberg, and Z. Tan. 2023. A new conjecture on hardness of 2-CSP’s with implications to hardness of densest k-subgraph and other problems. In Proceedings of the 14th Conference on Innovations in Theoretical Computer Science (ITCS’23). 38:1–38:23.

[59]

E. Cohen, E. Halperin, H. Kaplan, and U. Zwick. 2002. Reachability and distance queries via 2-hop labels. In Proceedings of the 13th Annual ACM–SIAM Symposium on Discrete Algorithms (SODA’02). 937–946.

[60]

L. Corinzia, P. Penna, W. Szpankowski, and J. Buhmann. 2022. Statistical and computational thresholds for the planted k-densest sub-hypergraph problem. In Proceedings of the 25th International Conference on Artificial Intelligence and Statistics (AISTATS’22). 11615–11640.

[61]

T. H. Cormen, C.E. Leiserson, R. L. Rivest, and C. Stein. 2022. Introduction to Algorithms, 4th edition. MIT Press.

[62]

G. Cormode, S. Muthukrishnan, K. Yi, and Q. Zhang. 2010. Optimal sampling from distributed streams. In Proceedings of the 29th ACM SIGMOD–SIGACT–SIGART Symposium on Principles of Database Systems (PODS’10). 77–86.

Digital Library

[63]

M. Cygan, F. V. Fomin, L. Kowalik, D. Lokshtanov, D. Marx, M. Pilipczuk, M. Pilipczuk, and S. Saurabh. 2015. Parameterized Algorithms. Springer.

[64]

A. D. Sarma, A. Lall, D. Nanongkai, and A. Trehan. 2012. Dense subgraphs on dynamic networks. In Proceedings of the 26th International Symposium on Distributed Computing (DISC’12). 151–165.

[65]

Y. Dai, M. Qiao, and L. Chang. 2022. Anchored densest subgraph. In Proceedings of the International Conference on Management of Data (SIGMOD’22). 1200–1213.

Digital Library

[66]

J. Ding and H. Du. 2023. Detection threshold for correlated Erdős-Rényi graphs via densest subgraph. IEEE Trans. Inf. Theory 69, 8 (2023), 5289–5298.

Digital Library

[67]

W. Dinkelbach. 1967. On nonlinear fractional programming. Manage. Sci. 13, 7 (1967), 492–498.

Digital Library

[68]

R. Dondi and M. M. Hosseinzadeh. 2021. Dense sub-networks discovery in temporal networks. SN Comput. Sci. 2, 3 (2021).

Digital Library

[69]

Y. Dourisboure, F. Geraci, and M. Pellegrini. 2007. Extraction and classification of dense communities in the web. In Proceedings of the 16th International Conference on World Wide Web (WWW’07). 461–470.

Digital Library

[70]

Y. Dourisboure, F. Geraci, and M. Pellegrini. 2009. Extraction and classification of dense implicit communities in the Web graph. ACM Trans. Web 3, 2 (2009), 1–36.

Digital Library

[71]

A. Epasto, S. Lattanzi, and M. Sozio. 2015. Efficient densest subgraph computation in evolving graphs. In Proceedings of the 24th International Conference on World Wide Web (WWW’15). 300–310.

Digital Library

[72]

H. Esfandiari, M. Hajiaghayi, and D.P. Woodruff. 2016. Brief announcement: Applications of uniform sampling: Densest subgraph and beyond. In Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA’16). 397–399.

Digital Library

[73]

H. Esfandiari and M. Mitzenmacher. 2018. Metric sublinear algorithms via linear sampling. In Proceedings of the IEEE Annual Symposium on Foundations of Computer Science (FOCS’18). 11–22.

[74]

L. Everett, L. S. Wang, and S. Hannenhalli. 2006. Dense subgraph computation via stochastic search: Application to detect transcriptional modules. Bioinformatics 22, 14 (2006), e117–e123.

Digital Library

[75]

Y. Fang, W. Luo, and C. Ma. 2022. Densest subgraph discovery on large graphs: Applications, challenges, and techniques. Proc. VLDB Endow. 15, 12 (2022), 3766–3769.

Digital Library

[76]

Y. Fang, K. Wang, X. Lin, and W. Zhang. 2022. Cohesive Subgraph Search over Large Heterogeneous Information Networks. Springer.

[77]

Y. Fang, K. Yu, R. Cheng, L.V.S. Lakshmanan, and X. Lin. 2019. Efficient algorithms for densest subgraph discovery. Proc. VLDB Endow. 12, 11 (2019), 1719–1732.

Digital Library

[78]

A. Faragó and Z.R. Mojaveri. 2019. In search of the densest subgraph. Algorithms 12, 8 (2019).

[79]

A. Fazzone, T. Lanciano, R. Denni, C. E. Tsourakakis, and F. Bonchi. 2022. Discovering polarization niches via dense subgraphs with attractors and repulsers. Proc. VLDB Endow. 15, 13 (Sep. 2022), 3883–3896.

Digital Library

[80]

U. Feige. 2002. Relations between average case complexity and approximation complexity. In Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC’02). 534–543.

Digital Library

[81]

U. Feige, G. Kortsarz, and D. Peleg. 2001. The dense k-subgraph problem. Algorithmica 29, 3 (2001), 410–421.

Digital Library

[82]

U. Feige and M. Langberg. 2001. Approximation algorithms for maximization problems arising in graph partitioning. J. Algor. 41, 2 (2001), 174–211.

Digital Library

[83]

U. Feige and M. Seltser. 1997. On the Densest k-subgraph Problem. Technical Report. Department of Applied Math and Computer Science, The Weizmann Institute.

Digital Library

[84]

J. Feng, R. Jiang, and T. Jiang. 2011. A max-flow-based approach to the identification of protein complexes using protein interaction and microarray data. IEEE/ACM Trans. Comput. Biol. Bioinf. 8, 3 (2011), 621–634.

Digital Library

[85]

W. Feng, S. Liu, D. Koutra, H. Shen, and X. Cheng. 2020. SpecGreedy: Unified dense subgraph detection. In Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD’20). 181–197.

[86]

S. Fortunato. 2010. Community detection in graphs. Phys. Rep. 486, 3-5 (2010), 75–174.

[87]

E. Fratkin, B.T. Naughton, D.L. Brutlag, and S. Batzoglou. 2006. MotifCut: Regulatory motifs finding with maximum density subgraphs. Bioinformatics 22, 14 (2006), e150–e157.

Digital Library

[88]

S. Fujishige. 2005. Submodular Functions and Optimization. Annals of Discrete Mathematics, Vol. 58. Elsevier.

[89]

A. Gajewar and A. Das Sarma. 2012. Multi-skill collaborative teams based on densest subgraphs. In Proceedings of the 2012 SIAM International Conference on Data Mining (SDM’12). 165–176.

[90]

E. Galimberti, F. Bonchi, and F. Gullo. 2017. Core decomposition and densest subgraph in multilayer networks. In Proceedings of the 26th ACM International Conference on Information and Knowledge Management (CIKM’17). 1807–1816.

Digital Library

[91]

E. Galimberti, F. Bonchi, F. Gullo, and T. Lanciano. 2020. Core decomposition in multilayer networks: Theory, algorithms, and applications. ACM Trans. Knowl. Discov. Data 14, 1 (2020), 1–40.

Digital Library

[92]

G. Gallo, M.D. Grigoriadis, and R.E. Tarjan. 1989. A fast parametric maximum flow algorithm and applications. SIAM J. Comput. 18, 1 (1989), 30–55.

Digital Library

[93]

S. Gao, R. H. Li, H. Qin, H. Chen, Y. Yuan, and G. Wang. 2022. Colorful h-star core decomposition. In Proceedings of the 38th IEEE International Conference on Data Engineering (ICDE’22). 2588–2601.

[94]

M. Ghaffari, Silvio Lattanzi, and S. Mitrović. 2019. Improved parallel algorithms for density-based network clustering. In Proceedings of the 36th International Conference on Machine Learning (ICML’19). 2201–2210.

[95]

D. Gibson, R. Kumar, and A. Tomkins. 2005. Discovering large dense subgraphs in massive graphs. In Proceedings of the 31st International Conference on Very Large Data Bases (VLDB’05). 721–732.

Digital Library

[96]

A. Gionis and C. E. Tsourakakis. 2015. Dense subgraph discovery: KDD 2015 tutorial. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’15). 2313–2314.

Digital Library

[97]

M. X. Goemans. 1996. Mathematical programming and approximation algorithms. Lecture at the Summer School on Approximate Solution of Hard Combinatorial Problems (1996).

[98]

A. V. Goldberg. 1984. Finding a Maximum Density Subgraph. Technical Report. University of California at Berkeley.

Digital Library

[99]

D. Goldstein and M. Langberg. 2009. The dense k subgraph problem. CoRR abs/0912.5327.

[100]

S. Gonzales and T. Migler. 2019. The densest k subgraph problem in b-outerplanar graphs. In Proceedings of the 8th International Conference on Complex Networks and Their Applications (COMPLEX NETWORKS’19). 116–127.

[101]

M. Grötschel, L. Lovász, and A. Schrijver. 1981. The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1, 2 (1981), 169–197.

[102]

N. V. C. Gudapati, E. Malaguti, and M. Monaci. 2021. In search of dense subgraphs: How good is greedy peeling? Networks 77, 4 (2021), 572–586.

[103]

T. Hanaka. 2023. Computing densest k-subgraph with structural parameters. J. Combin. Optim. 45, 1 (2023), 1–17.

Digital Library

[104]

E. Harb, K. Quanrud, and C. Chekuri. 2022. Faster and scalable algorithms for densest subgraph and decomposition. In Proceedings of the 36th Conference on Neural Information Processing Systems (NeurIPS’22).

[105]

E. Harb, K. Quanrud, and C. Chekuri. 2023. Convergence to lexicographically optimal base in a (contra)polymatroid and applications to densest subgraph and tree packing. arXiv:2305.02987. Retrieved from https://arxiv.org/abs/2305.02987

[106]

F. Hashemi, A. Behrouz, and L.V.S. Lakshmanan. 2022. FirmCore decomposition of multilayer networks. In Proceedings of the ACM Web Conference 2022 (TheWebConf’22). 1589–1600.

Digital Library

[107]

R. Hassin, S. Rubinstein, and A. Tamir. 1997. Approximation algorithms for maximum dispersion. Operat. Res. Lett. 21, 3 (1997), 133–137.

Digital Library

[108]

E. Hazan and R. Krauthgamer. 2011. How hard is it to approximate the best nash equilibrium? SIAM J. Comput. 40, 1 (2011), 79–91.

Digital Library

[109]

M. Henzinger, A. Paz, and A. R. Sricharan. 2022. Fine-grained complexity lower bounds for families of dynamic graphs. In Proceedings of the 30th Annual European Symposium on Algorithms (ESA’22). 65:1–65:14.

[110]

D. S. Hochbaum. 2008. The pseudoflow algorithm: A new algorithm for the maximum-flow problem. Operat. Res. 56, 4 (2008), 992–1009.

Digital Library

[111]

B. Hooi, H.A. Song, A. Beutel, N. Shah, K. Shin, and C. Faloutsos. 2016. FRAUDAR: Bounding graph fraud in the face of camouflage. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’16). 895–904.

Digital Library

[112]

H. Hu, X. Yan, Y. Huang, J. Han, and X. J. Zhou. 2005. Mining coherent dense subgraphs across massive biological networks for functional discovery. Bioinformatics 21, 1 (2005), i213–i221.

[113]

S. Hu, X. Wu, and T. H. H. Chan. 2017. Maintaining densest subsets efficiently in evolving hypergraphs. In Proceedings of the ACM on Conference on Information and Knowledge Management (CIKM’17). Association for Computing Machinery, New York, NY, 929–938.

Digital Library

[114]

D. J. H. Huang and A. B. Kahng. 1995. When clusters meet partitions: New density-based methods for circuit decomposition. In Proceedings of the 1995 IEEE European Design and Test Conference (EDTC’95). 60–64.

[115]

Y. Huang, D.F. Gleich, and N. Veldt. 2023. Densest subhypergraph: Negative supermodular functions and strongly localized methods. arXiv:2310.13792. Retrieved from https://arxiv.org/abs/2310.13792

[116]

R. Impagliazzo and R. Paturi. 2001. On the complexity of k-SAT. J. Comput. Syst. Sci. 62, 2 (2001), 367–375.

Digital Library

[117]

S. Iwata, L. Fleischer, and S. Fujishige. 2001. A combinatorial strongly polynomial algorithm for minimizing submodular functions. J. ACM 48, 4 (2001), 761–777.

Digital Library

[118]

J. JéJé. 1992. An Introduction to Parallel Algorithms. Addison-Wesley.

[119]

V. Jethava and N. Beerenwinkel. 2015. Finding dense subgraphs in relational graphs. In Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD’15). 641–654.

[120]

Y. Ji, Z. Zhang, X. Tang, J. Shen, X. Zhang, and G. Yang. 2022. Detecting cash-out users via dense subgraphs. In Proceedings of the 28th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’22). 687–697.

Digital Library

[121]

J. Jiang, Y. Li, B. He, B. Hooi, J. Chen, and J. K. Z. Kang. 2022. Spade: A real-time fraud detection framework on evolving graphs. Proc. VLDB Endow. 16, 3 (2022), 461–469.

Digital Library

[122]

R. Jin, Y. Xiang, N. Ruan, and D. Fuhry. 2009. 3-HOP: A high-compression indexing scheme for reachability query. In Proceedings of the International Conference on Management of Data (SIGMOD’09). 813–826.

Digital Library

[123]

S. Kamara and T. Moataz. 2019. Computationally volume-hiding structured encryption. In Proceedings of the 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT’19). 183–213.

Digital Library

[124]

R. Kannan and V. Vinay. 1999. Analyzing the Structure of Large Graphs.Technical Report. Institut für Ökonometrie und Operations Research, Universität Bonn.

[125]

Y. Kawase, Y. Kuroki, and A. Miyauchi. 2019. Graph mining meets crowdsourcing: Extracting experts for answer aggregation. In Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI’19). 1272–1279.

[126]

Y. Kawase and A. Miyauchi. 2018. The densest subgraph problem with a convex/concave size function. Algorithmica 80, 12 (2018), 3461–3480.

[127]

Y. Kawase, A. Miyauchi, and H. Sumita. 2023. Stochastic solutions for dense subgraph discovery in multilayer networks. In Proceedings of the 16th ACM International Conference on Web Search and Data Mining (WSDM’23). 886–894.

Digital Library

[128]

Y. Khanna and A. Louis. 2020. Planted models for the densest k-subgraph problem. In Proceedings of the 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS’20). 27:1–27:18.

[129]

S. Khot. 2006. Ruling out PTAS for graph min-bisection, dense k-subgraph, and bipartite clique. SIAM J. Comput. 36, 4 (2006), 1025–1071.

Digital Library

[130]

S. Khuller and B. Saha. 2009. On finding dense subgraphs. In Proceedings of the 36th International Colloquium on Automata, Languages and Programming (ICALP’09). 597–608.

Digital Library

[131]

J. Kim, T. Guo, K. Feng, G. Cong, A. Khan, and F. M. Choudhury. 2020. Densely connected user community and location cluster search in location-based social networks. In Proceedings of the International Conference on Management of Data (SIGMOD’20). 2199–2209.

Digital Library

[132]

C. Komusiewicz and F. Sommer. 2020. FixCon: A generic solver for fixed-cardinality subgraph problems. In Proceedings of the SIAM Symposium on Algorithm Engineering and Experiments (ALENEX’20). 12–26.

[133]

C. Komusiewicz and M. Sorge. 2015. An algorithmic framework for fixed-cardinality optimization in sparse graphs applied to dense subgraph problems. Discr. Appl. Math. 193 (2015), 145–161.

Digital Library

[134]

A. Konar and N. D. Sidiropoulos. 2021. Exploring the subgraph density-size trade-off via the Lovaśz extension. In Proceedings of the 14th ACM International Conference on Web Search and Data Mining (WSDM’21). 743–751.

Digital Library

[135]

A. Konar and N. D. Sidiropoulos. 2022. The triangle-densest-k-subgraph problem: Hardness, Lovász extension, and application to document summarization. In Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI’22). 4075–4082.

[136]

G. Kortsarz and D. Peleg. 1994. Generating sparse 2-spanners. J. Algor. 17, 2 (1994), 222–236.

Digital Library

[137]

M. Koutrouli, E. Karatzas, D. Paez-Espino, and G.A. Pavlopoulos. 2020. A guide to conquer the biological network era using graph theory. Front. Bioeng. Biotechnol. 8, 34 (2020), 1–34.

[138]

N. Krislock, J. Malick, and F. Roupin. 2016. Computational results of a semidefinite branch-and-bound algorithm for k-cluster. Comput. Operat. Res. 66 (2016), 153–159.

Digital Library

[139]

Y. Kuroki, A. Miyauchi, J. Honda, and M. Sugiyama. 2020. Online dense subgraph discovery via blurred-graph feedback. In Proceedings of the 37th International Conference on Machine Learning (ICML’20). 5522–5532.

Digital Library

[140]

M. Lampis. 2012. Algorithmic meta-theorems for restrictions of treewidth. Algorithmica 64 (2012), 19–37.

[141]

T. Lanciano, F. Bonchi, and A. Gionis. 2020. Explainable classification of brain networks via contrast subgraphs. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’20). 3308–3318.

Digital Library

[142]

T. Lanciano, A. Savino, F. Porcu, D. Cittaro, F. Bonchi, and P. Provero. 2023. Contrast subgraphs allow comparing homogeneous and heterogeneous networks derived from omics data. GigaScience 12 (2023), 1–10.

[143]

V. E. Lee, N. Ruan, R. Jin, and C. Aggarwal. 2010. A Survey of Algorithms for Dense Subgraph Discovery. Springer US, Boston, MA, 303–336.

[144]

Y. T. Lee, A. Sidford, and S. C. W. Wong. 2015. A faster cutting plane method and its implications for combinatorial and convex optimization. In Proceedings of the IEEE Annual Symposium on Foundations of Computer Science (FOCS’15). 1049–1065.

Digital Library

[145]

R. Li, J.Y. Lee, J. M. Yang, and T. Akutsu. 2022. Densest subgraph-based methods for protein-protein interaction hot spot prediction. BMC Bioinf. 23, 451 (2022).

[146]

R. Li and K. Quanrud. 2023. Approximate Fully Dynamic Directed Densest Subgraph. arxiv:2312.07827 [cs.DS]. Retrieved from https://arxiv.org/abs/2312.07827

[147]

X. Li, S. Liu, Z. Li, X. Han, C. Shi, B. Hooi, H. Huang, and X. Cheng. 2020. FlowScope: Spotting money laundering based on graphs. In Proceedings of the 34th AAAI Conference on Artificial Intelligence (AAAI’20). 4731–4738.

[148]

M. Liazi, I. Milis, and V. Zissimopoulos. 2008. A constant approximation algorithm for the densest k-subgraph problem on chordal graphs. Inform. Process. Lett. 108, 1 (2008), 29–32.

Digital Library

[149]

X. Liu, T. Ge, and Y. Wu. 2022. A stochastic approach to finding densest temporal subgraphs in dynamic graphs. IEEE Trans. Knowl. Data Eng. 34, 7 (2022), 3082–3094.

[150]

W. Luo, Z. Tang, Y. Fang, C. Ma, and X. Zhou. 2023. Scalable algorithms for densest subgraph discovery. In Proceedings of the 39th IEEE International Conference on Data Engineering (ICDE’23). 285–298.

[151]

P. C. Lusk, K. Fathian, and J. P. How. 2021. CLIPPER: A graph-theoretic framework for robust data association. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA’21). 13828–13834.

Digital Library

[152]

C. Ma, R. Cheng, L.V.S. Lakshmanan, and X. Han. 2022. Finding locally densest subgraphs: A convex programming approach. Proc. VLDB Endow. 15, 11 (2022), 2719–2732.

Digital Library

[153]

C. Ma, Y. Fang, R. Cheng, L. V. S. Lakshmanan, and X. Han. 2022. A convex-programming approach for efficient directed densest subgraph discovery. In Proceedings of the International Conference on Management of Data (SIGMOD’22). Association for Computing Machinery, New York, NY, 845–859.

Digital Library

[154]

C. Ma, Y. Fang, R. Cheng, L. V. S. Lakshmanan, W. Zhang, and X. Lin. 2020. Efficient algorithms for densest subgraph discovery on large directed graphs. In Proceedings of the International Conference on Management of Data (SIGMOD’20). 1051–1066.

Digital Library

[155]

C. Ma, Y. Fang, R. Cheng, L. V. S. Lakshmanan, W. Zhang, and X. Lin. 2021. Efficient directed densest subgraph discovery. SIGMOD Rec. 50, 1 (Jun.2021), 33–40.

Digital Library

[156]

C. Ma, Y. Fang, R. Cheng, L. V. S. Lakshmanan, W. Zhang, and X. Lin. 2021. On directed densest subgraph discovery. ACM Trans. Database Syst. 46, 4, Article 13 (Nov.2021), 45 pages.

Digital Library

[157]

S. Ma, R. Hu, L. Wang, X. Lin, and J. Huai. 2020. An efficient approach to finding dense temporal subgraphs. IEEE Trans. Knowl. Data Eng. 32, 4 (2020), 645–658.

[158]

W. Mader. 1972. Existenzn-fach zusammenhängender Teilgraphen in Graphen genügend großer Kantendichte. Abhandlung. Math. Semin. Univ. Hamburg 37, 1 (1972), 86–97.

[159]

K. Majbouri Yazdi, A. Majbouri Yazdi, S. Khodayi, J. Hou, W. Zhou, S. Saedy, and M. Rostami. 2020. Prediction optimization of diffusion paths in social networks using integration of ant colony and densest subgraph algorithms. J. High Speed Netw. 26, 2 (2020), 141–153.

Digital Library

[160]

J. Malick and F. Roupin. 2012. Solving k-cluster problems to optimality with semidefinite programming. Math. Program. 136, 2 (2012), 279–300.

Digital Library

[161]

F. D. Malliaros, C. Giatsidis, A. N. Papadopoulos, and M. Vazirgiannis. 2020. The core decomposition of networks: Theory, algorithms and applications. VLDB J. 29 (2020), 61–92.

Digital Library

[162]

F. D. Malliaros and M. Vazirgiannis. 2013. Clustering and community detection in directed networks: A survey. Phys. Rep. 533, 4 (2013), 95–142.

[163]

P. Manurangsi. 2017. Almost-polynomial ratio ETH-hardness of approximating densest k-subgraph. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (STOC’17). 954–961.

Digital Library

[164]

L. Martini, A. Fazzone, M. Gentili, L. Becchetti, and B. Hobbs. 2022. Network based approach to gene prioritization at genome-wide association study loci. CoRR abs/2210.16292.

[165]

A. McGregor, D. Tench, S. Vorotnikova, and H. T. Vu. 2015. Densest subgraph in dynamic graph streams. In Proceedings of the 40th International Symposium on Mathematical Foundations of Computer Science (MFCS’15). 472–482.

[166]

M. Mitzenmacher, J. Pachocki, R. Peng, C. E. Tsourakakis, and S. C. Xu. 2015. Scalable large near-clique detection in large-scale networks via sampling. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’15). 815–824.

Digital Library

[167]

A. Miyauchi, T. Chen, K. Sotiropoulos, and C. E. Tsourakakis. 2023. Densest diverse subgraphs: How to plan a successful cocktail party with diversity. In Proceedings of the 29th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’23). 1710–1721.

Digital Library

[168]

A. Miyauchi, Y. Iwamasa, T. Fukunaga, and N. Kakimura. 2015. Threshold influence model for allocating advertising budgets. In Proceedings of the 32nd International Conference on Machine Learning (ICML’15). 1395–1404.

[169]

A. Miyauchi and N. Kakimura. 2018. Finding a dense subgraph with sparse cut. In Proceedings of the 27th ACM International Conference on Information and Knowledge Management (CIKM’18). 547–556.

Digital Library

[170]

A. Miyauchi and A. Takeda. 2018. Robust densest subgraph discovery. In Proceedings of the 18th IEEE International Conference on Data Mining (ICDM’18). 1188–1193.

[171]

Y. Mizutani and B. D. Sullivan. 2022. Parameterized complexity of maximum happy set and densest k-subgraph. In Proceedings of the 17th International Symposium on Parameterized and Exact Computation (IPEC’22). 23:1–23:18.

[172]

A. Moro, A. Raganato, and R. Navigli. 2014. Entity linking meets word sense disambiguation: A unified approach. Trans. Assoc. Comput. Ling. 2 (2014), 231–244.

[173]

K. Nagano, Y. Kawahara, and K. Aihara. 2011. Size-constrained submodular minimization through minimum norm base. In Proceedings of the 28th International Conference on Machine Learning (ICML’11). 977–984.

[174]

M. C. V. Nascimento and A. C. P. L. F. de Carvalho. 2011. Spectral methods for graph clustering—A survey. Eur. J. Operat. Res. 211, 2 (2011), 221–231.

[175]

J. B. Orlin. 2009. A faster strongly polynomial time algorithm for submodular function minimization. Math. Program. 118, 2 (2009), 237–251.

Digital Library

[176]

D. Papailiopoulos, I. Mitliagkas, A. Dimakis, and C. Caramanis. 2014. Finding dense subgraphs via low-rank bilinear optimization. In Proceedings of the 31st International Conference on Machine Learning (ICML’14). 1890–1898.

[177]

D. Peleg. 2000. Distributed Computing: A Locality-Sensitive Approach. Society for Industrial and Applied Mathematics.

[178]

J. C. Picard and M. Queyranne. 1982. A network flow solution to some nonlinear 0-1 programming problems, with applications to graph theory. Networks 12, 2 (1982), 141–159.

[179]

M. Potamias, F. Bonchi, A. Gionis, and G. Kollios. 2010. k-nearest neighbors in uncertain graphs. Proc. VLDB Endow. 3, 1 (2010), 997–1008.

Digital Library

[180]

H. Qin, R.H. Li, Y. Yuan, Y. Dai, and G. Wang. 2023. Densest periodic subgraph mining on large temporal graphs. IEEE Trans. Knowl. Data Eng. 35, 11 (2023), 11259–11273.

Digital Library

[181]

P. Raghavendra and D. Steurer. 2010. Graph expansion and the unique games conjecture. In Proceedings of the 42nd Annual ACM Symposium on Theory of Computing (STOC’10). 755–764.

Digital Library

[182]

S. S. Rangapuram, T. Bühler, and M. Hein. 2013. Towards realistic team formation in social networks based on densest subgraphs. In Proceedings of the 22nd International Conference on World Wide Web (WWW’13). 1077–1088.

Digital Library

[183]

S. S. Ravi, D. J. Rosenkrantz, and G. K. Tayi. 1994. Heuristic and special case algorithms for dispersion problems. Operat. Res. 42, 2 (1994), 299–310.

Digital Library

[184]

A. Reinthal, A. Törnqvist, A. Andersson, E. Norlander, P. Stålhammar, and S. Norlin. 2016. Finding the Densest Common Subgraph with Linear Programming. B.S. thesis. Chalmers University of Technology & University of Gothenburg.

[185]

Y. Ren, H. Zhu, J. Zhang, P. Dai, and L. Bo. 2021. EnsemFDet: An ensemble approach to fraud detection based on bipartite graph. In Proceedings of the 37th IEEE International Conference on Data Engineering (ICDE’21). 2039–2044.

[186]

P. Rozenshtein, A. Anagnostopoulos, A. Gionis, and N. Tatti. 2014. Event detection in activity networks. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’14). 1176–1185.

Digital Library

[187]

P. Rozenshtein, F. Bonchi, A. Gionis, M. Sozio, and N. Tatti. 2019. Finding events in temporal networks: Segmentation meets densest subgraph discovery. Knowl. Inf. Syst. 62, 4 (2019), 1611–1639.

Digital Library

[188]

P. Rozenshtein, G. Preti, A. Gionis, and Y. Velegrakis. 2020. Mining dense subgraphs with similar edges. In Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD’20). 20–36.

[189]

P. Rozenshtein, N. Tatti, and A. Gionis. 2017. Finding dynamic dense subgraphs. ACM Trans. Knowl. Discov. Data 11, 3 (2017), 1–30.

Digital Library

[190]

A. Saha, X. Ke, A. Khan, and C. Long. 2023. Most probable densest subgraphs. In Proceedings of the 39th IEEE International Conference on Data Engineering (ICDE’23). 1447–1460.

[191]

C. Ma. 2019. Supplementary note for “efficient algorithms for densest subgraph discovery on large directed graphs”. https://i.cs.hku.hk/%7Echma2/sup-sigmod2020.pdf

[192]

B. Saha, A. Hoch, S. Khuller, L. Raschid, and X. N. Zhang. 2010. Dense subgraphs with restrictions and applications to gene annotation graphs. In Proceedings of the 14th Annual International Conference on Research in Computational Molecular Biology (RECOMB’10). 456–472.

Digital Library

[193]

A. E. Sarıyüce, C. Seshadhri, A. Pinar, and U. V. Çatalyürek. 2015. Finding the hierarchy of dense subgraphs using nucleus decompositions. In Proceedings of the 24th International Conference on World Wide Web (WWW’15). 927–937.

Digital Library

[194]

A. E. Sarıyüce, C. Seshadhri, A. Pinar, and U. V. Çatalyürek. 2017. Nucleus decompositions for identifying hierarchy of dense subgraphs. ACM Trans. Web 11, 3 (2017), 16:1–16:27.

Digital Library

[195]

A. E. Sarıyüce and A. Pinar. 2018. Peeling bipartite networks for dense subgraph discovery. In Proceedings of the 11th ACM International Conference on Web Search and Data Mining (WSDM’18). 504–512.

Digital Library

[196]

S. Sawlani and J. Wang. 2020. Near-optimal fully dynamic densest subgraph. In Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing (STOC’20). 181–193.

Digital Library

[197]

S. E. Schaeffer. 2007. Graph clustering. Comput. Sci. Rev. 1, 1 (2007), 27–64.

Digital Library

[198]

A. Schrijver. 2000. A combinatorial algorithm minimizing submodular functions in strongly polynomial time. J. Combin. Theory Ser. B 80, 2 (2000), 346–355.

Digital Library

[199]

K. Semertzidis, E. Pitoura, E. Terzi, and P. Tsaparas. 2019. Finding lasting dense subgraphs. Data Min. Knowl. Discov. 33, 5 (2019), 1417–1445.

Digital Library

[200]

S. Shahinpour and S. Butenko. 2013. Distance-based clique relaxations in networks: s-clique and s-club. In Models, Algorithms, and Technologies for Network Analysis, B. I. Goldengorin, V. A. Kalyagin, and P. M. Pardalos (Eds.). 149–174.

[201]

J. Shi, L. Dhulipala, and J. Shun. 2021. Parallel clique counting and peeling algorithms. In Proceedings of the SIAM Conference on Applied and Computational Discrete Algorithms (ACDA). 135–146.

[202]

K. Shin, B. Hooi, and C. Faloutsos. 2016. M-zoom: Fast dense-block detection in tensors with quality guarantees. In Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD’16). 264–280.

Digital Library

[203]

K. Shin, B. Hooi, J. Kim, and C. Faloutsos. 2017. D-cube: Dense-block detection in terabyte-scale tensors. In Proceedings of the 10th ACM International Conference on Web Search and Data Mining (WSDM’17). 681–689.

Digital Library

[204]

K. Shin, B. Hooi, J. Kim, and C. Faloutsos. 2017. DenseAlert: Incremental dense-subtensor detection in tensor streams. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’17). 1057–1066.

Digital Library

[205]

R. Sotirov. 2020. On solving the densest k-subgraph problem on large graphs. Optim. Methods Softw. 35, 6 (2020), 1160–1178.

[206]

M. Sozio and A. Gionis. 2010. The community-search problem and how to plan a successful cocktail party. In Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’10). 939–948.

Digital Library

[207]

H. H. Su and H. T. Vu. 2020. Distributed dense subgraph detection and low outdegree orientation. In Proceedings of the 34th International Symposium on Distributed Computing (DISC’20). 15:1–15:18.

[208]

I. Sukeda, A. Miyauchi, and A. Takeda. 2023. A study on modularity density maximization: Column generation acceleration and computational complexity analysis. Eur. J. Operat. Res. 309, 2 (2023), 516–528.

[209]

B. Sun, M. Danisch, T.-H. Hubert Chan, and M. Sozio. 2020. KClist++: A simple algorithm for finding k-Clique Densest Subgraphs in Large Graphs. Proc. VLDB Endow. 13, 10 (2020).

Digital Library

[210]

Z. Sun, X. Huang, J. Xu, and F. Bonchi. 2021. Efficient probabilistic truss indexing on uncertain graphs. In Proceedings of the ACM Web Conference 2021 (TheWebConf’21). 354–366.

Digital Library

[211]

R. G. Sundaram, H. Gupta, and C. R. Ramakrishnan. 2021. Efficient distribution of quantum circuits. In Proceedings of the 35th International Symposium on Distributed Computing (DISC’21). 41:1–41:20.

[212]

S. Suri and S. Vassilvitskii. 2011. Counting triangles and the curse of the last reducer. In Proceedings of the 20th International Conference on World Wide Web (WWW’11). 607–614.

Digital Library

[213]

X. Tan, M. Zhou, and B. Fitzgerald. 2020. Scaling open source communities: An empirical study of the linux kernel. In Proceedings of the 42nd International Conference on Software Engineering (ICSE’20). 1222–1234.

Digital Library

[214]

C. E. Tsourakakis. 2015. The k-clique densest subgraph problem. In Proceedings of the 24th International Conference on World Wide Web (WWW’15). 1122–1132.

Digital Library

[215]

C. E. Tsourakakis, F. Bonchi, A. Gionis, F. Gullo, and M. A. Tsiarli. 2013. Denser than the densest subgraph: Extracting optimal quasi-cliques with quality guarantees. In Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’13). 104–112.

Digital Library

[216]

C. E. Tsourakakis, T. Chen, N. Kakimura, and J. Pachocki. 2019. Novel dense subgraph discovery primitives: Risk aversion and exclusion queries. In Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD’19). 378–394.

[217]

N. Veldt, A. R. Benson, and J. Kleinberg. 2021. The generalized mean densest subgraph problem. In Proceedings of the 27th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’21). 1604–1614.

Digital Library

[218]

N. Veldt, A. R. Benson, and J. Kleinberg. 2022. Hypergraph cuts with general splitting functions. SIAM Rev. 64, 3 (2022), 650–685.

Digital Library

[219]

Q. Wu and J.K. Hao. 2015. A review on algorithms for maximum clique problems. Eur. J. Operat. Res. 242, 3 (2015), 693–709.

[220]

Q. Wu, X. Huang, A. J. Culbreth, J. A. Waltz, L. E. Hong, and S. Chen. 2021. Extracting brain disease-related connectome subgraphs by adaptive dense subgraph discovery. Biometrics 78, 4 (2021), 1566–1578.

[221]

Y. Wu, R. Jin, X. Zhu, and X. Zhang. 2015. Finding dense and connected subgraphs in dual networks. In Proceedings of the 31st IEEE International Conference on Data Engineering (ICDE’15). 915–926.

[222]

Y. Wu, X. Zhu, L. Li, W. Fan, R. Jin, and X. Zhang. 2016. Mining dual networks: Models, algorithms, and applications. ACM Trans. Knowl. Discov. Data 10, 4 (2016), 40:1–40:37.

Digital Library

[223]

T. Xie, Y. Zhang, and D. Song. 2022. Orion: Zero knowledge proof with linear prover time. In Proceedings of the 42nd Annual International Cryptology Conference (CRYPT’22). 299–328.

Digital Library

[224]

H. Yan, Q. Zhang, D. Mao, Z. Lu, D. Guo, and S. Chen. 2021. Anomaly detection of network streams via dense subgraph discovery. In Proceedings of the 30th International Conference on Computer Communications and Networks (ICCCN’21). 1–9.

[225]

H. Yanagisawa and S. Hara. 2018. Discounted average degree density metric and new algorithms for the densest subgraph problem. Networks 71, 1 (2018), 3–15.

[226]

Y. Yang, L. Chu, Y. Zhang, Z. Wang, J. Pei, and E. Chen. 2018. Mining density contrast subgraphs. In Proceedings of the 34th IEEE International Conference on Data Engineering (ICDE’18). 221–232.

[227]

Y. Ye and J. Zhang. 2003. Approximation of dense-\(n/2\)-subgraph and the complement of min-bisection. J. Glob. Optim. 25, 1 (2003), 55–73.

Digital Library

[228]

B. Yikun, L. Xin, H. Ling, D. Yitao, L. Xue, and X. Wei. 2019. No place to hide: Catching fraudulent entities in tensors. In Proceedings of the ACM Web Conference (TheWebConf’19). 83–93.

Digital Library

[229]

P. Zhang and Z. Liu. 2021. Approximating max k-uncut via LP-rounding plus greed, with applications to densest k-subgraph. Theor. Comput. Sci. 849, 6 (2021), 173–183.

[230]

Y. Zhou, S. Hu, and Z. Sheng. 2022. Extracting densest sub-hypergraph with convex edge-weight functions. In Proceedings of the 17th Annual Conference on Theory and Applications of Models of Computation (TAMC’22). 305–321.

Digital Library

[231]

C. X. Zhu, L. L. Lin, P. P. Yuan, and H. Jin. 2022. Discovering cohesive temporal subgraphs with temporal density aware exploration. J. Comput. Sci. Technol. 37, 5 (2022), 1068–1085.

Digital Library

[232]

Z. Zou. 2013. Polynomial-time algorithm for finding densest subgraphs in uncertain graphs. In Proceedings of the 11th Workshop on Mining and Learning with Graphs (MLG’13).

Cited By

Chen TMiyauchi ATsourakakis CNejdl WAuer SKarras OCha MMoens MNajork M(2025)Q-DISCO: Query-Centric Densest Subgraphs in Networks with Opinion InformationProceedings of the Eighteenth ACM International Conference on Web Search and Data Mining10.1145/3701551.3703502(194-203)Online publication date: 10-Mar-2025
https://dl.acm.org/doi/10.1145/3701551.3703502
Yuan ZSun QZhou HShao MFu X(2025)A comprehensive survey on GNN-based anomaly detection: taxonomy, methods, and the role of large language modelsInternational Journal of Machine Learning and Cybernetics10.1007/s13042-024-02516-6Online publication date: 4-Feb-2025
https://doi.org/10.1007/s13042-024-02516-6
Dhawan AMao CWein A(2025)Detection of Dense Subhypergraphs by Low‐Degree PolynomialsRandom Structures & Algorithms10.1002/rsa.2127966:1Online publication date: 20-Jan-2025
https://doi.org/10.1002/rsa.21279
Show More Cited By

Index Terms

A Survey on the Densest Subgraph Problem and its Variants
1. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis

Recommendations

Constant factor approximation algorithms for the densest k-subgraph problem on proper interval graphs and bipartite permutation graphs

The densest k-subgraph problem asks for a k-vertex subgraph with the maximum number of edges. This problem is NP-hard on bipartite graphs, chordal graphs, and planar graphs. A 3-approximation algorithm is known for chordal graphs. We present 32-...
Sandwiching a densest subgraph by consecutive cores

In this paper, we show that in the random graph Gn,c/n, with high probability, there exists an integer kï such that a subgraph of Gn,c/n, whose vertex set differs from a densest subgraph of Gn,c/n by Olog2n vertices, is sandwiched by the kï and the kï +...
Finding densest k-connected subgraphs
Abstract
Dense subgraph discovery is an important graph-mining primitive with a variety of real-world applications. One of the most well-studied optimization problems for dense subgraph discovery is the densest subgraph problem, where given an ...

Comments

Information & Contributors

Information

Published In

cover image ACM Computing Surveys

ACM Computing Surveys Volume 56, Issue 8

August 2024

963 pages

EISSN:1557-7341

DOI:10.1145/3613627

Editors:
David Atienza
Swiss Federal Institute of Technology Lausanne (EPFL), Switzerland
,
Michela Milano
University of Bologna, Italy

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 30 April 2024

Online AM: 22 March 2024

Accepted: 07 March 2024

Revised: 21 January 2024

Received: 28 March 2023

Published in CSUR Volume 56, Issue 8

Check for updates

Author Tags

Qualifiers

Survey

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

10
Total Citations
View Citations
909
Total Downloads

Downloads (Last 12 months)909
Downloads (Last 6 weeks)141

Reflects downloads up to 03 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

Chen TMiyauchi ATsourakakis CNejdl WAuer SKarras OCha MMoens MNajork M(2025)Q-DISCO: Query-Centric Densest Subgraphs in Networks with Opinion InformationProceedings of the Eighteenth ACM International Conference on Web Search and Data Mining10.1145/3701551.3703502(194-203)Online publication date: 10-Mar-2025
https://dl.acm.org/doi/10.1145/3701551.3703502
Yuan ZSun QZhou HShao MFu X(2025)A comprehensive survey on GNN-based anomaly detection: taxonomy, methods, and the role of large language modelsInternational Journal of Machine Learning and Cybernetics10.1007/s13042-024-02516-6Online publication date: 4-Feb-2025
https://doi.org/10.1007/s13042-024-02516-6
Dhawan AMao CWein A(2025)Detection of Dense Subhypergraphs by Low‐Degree PolynomialsRandom Structures & Algorithms10.1002/rsa.2127966:1Online publication date: 20-Jan-2025
https://doi.org/10.1002/rsa.21279
Feng WWang LHooi BNg SLiu S(2024)Interrelated Dense Pattern Detection in Multilayer NetworksIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2024.339868336:11(6462-6476)Online publication date: Nov-2024
https://doi.org/10.1109/TKDE.2024.3398683
Zhao CAl-Bashabsheh AChan C(2024)Detecting Informationally-Dense Subsets2024 IEEE Information Theory Workshop (ITW)10.1109/ITW61385.2024.10806913(771-776)Online publication date: 24-Nov-2024
https://doi.org/10.1109/ITW61385.2024.10806913
Liu DWang RZou ZHuang X(2024)Fast Multilayer Core Decomposition and Indexing2024 IEEE 40th International Conference on Data Engineering (ICDE)10.1109/ICDE60146.2024.00211(2695-2708)Online publication date: 13-May-2024
https://doi.org/10.1109/ICDE60146.2024.00211
Wickrama Arachchi CTatti N(2024)Jaccard-constrained dense subgraph discoveryMachine Learning10.1007/s10994-024-06595-yOnline publication date: 23-Jul-2024
https://doi.org/10.1007/s10994-024-06595-y
He TLiu STawarmalani M(2024)Convexification techniques for fractional programsMathematical Programming10.1007/s10107-024-02131-xOnline publication date: 16-Aug-2024
https://doi.org/10.1007/s10107-024-02131-x
Pan DZhou XLuo WYang ZLiu QGao YLi K(2024)Accelerating maximum biplex search over large bipartite graphsThe VLDB Journal10.1007/s00778-024-00882-934:1Online publication date: 26-Nov-2024
https://doi.org/10.1007/s00778-024-00882-9
Behrouz AHashemi F(2024)Generalized Densest Subgraph in Multiplex NetworksComplex Networks & Their Applications XII10.1007/978-3-031-53472-0_5(49-61)Online publication date: 21-Feb-2024
https://doi.org/10.1007/978-3-031-53472-0_5

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Full Text

View this article in Full Text.

Figures

Tables

Media

View full text|Download PDF

View Issue’s Table of Contents