Abstract
One of the classic problems related to graphs is partitioning their vertices into subsets, consisting of composing groups with high connectivity. The graph partitioning problem is of interest since the amount of data generated today is gigantic, and the importance of determining groups is essential for making strategic decisions in several areas. This paper compares the main graph partitioning methods found in the literature, considering the minimum cut criteria and load balancing factors in different types of graphs.
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References
R. Battiti, A. Bertossi, Differential greedy for the 0-1 equicut problem, in Proceedings of the DIMACS Workshop on Network Design: Connectivity and Facilities Location (1997) , pp. 3–21
R. Battiti, A.A. Bertossi, Greedy, prohibition, and reactive heuristics for graph partitioning. IEEE Trans. Comput. 48(4), 361–385 (1999)
V.D. Blondel, J.L. Guillaume, R. Lambiotte, E. Lefebvre, Fast unfolding of communities in large networks. J. Stat. Mech. Theory Experiment 2008(10), P10008 (2008)
Ü. Çatalyürek, K. Devine, M. Faraj, L. Gottesbüren, T. Heuer, H. Meyerhenke, P. Sanders, S. Schlag, C. Schulz, D. Seemaier et al., More recent advances in (hyper) graph partitioning. ACM Comput. Surv. 55(12), 1–38 (2023)
T.F. Chan, P. Ciarlet Jr., W. Szeto, On the optimality of the median cut spectral bisection graph partitioning method. SIAM J. Sci. Comput. 18(3), 943–948 (1997)
I.A. Ebeid, J.R. Talburt, M.A.S. Siddique, Graph-based hierarchical record clustering for unsupervised entity resolution, in 19th ITNG (2022), pp. 107–118
J. Edmonds, Matroids and the greedy algorithm. Math. Program. 1(1), 127–136 (1971)
C.M. Fiduccia, R.M. Mattheyses, A linear-time heuristic for improving network partitions, in Design Automation, 1982. 19th Conference on (IEEE, 1982), pp. 175–181
M. Hajiaghayi, T. Johnson, M.R. Khani, B. Saha, Hierarchical graph partitioning, in Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures (2014), pp. 51–60
P. Hansen, M. Delattre, Complete-link cluster analysis by graph coloring. J. Am. Stat. Assoc. 73(362), 397–403 (1978)
D. Hausmann, B. Korte, K-greedy algorithms for independence systems. Z. Oper. Res. 22(1), 219–228 (1978)
B. Hendrickson, R.W. Leland, A multi-level algorithm for partitioning graphs. SC 95, 28 (1995)
A.K. Jain, R.C. Dubes, Algorithms for Clustering Data (Prentice-Hall, 1988)
G. Karypis, V. Kumar, Multilevel graph partitioning schemes, in ICPP (3) (1995), pp. 113–122
B.W. Kernighan, S. Lin, An efficient heuristic procedure for partitioning graphs. Bell Syst. Tech. J. 49(2), 291–307 (1970)
A.A. Khan, M.U. Khan, M. Iqbal, Multilevel graph partitioning scheme to solve traveling salesman problem, in 9th ITNG (2012), pp. 458–463
N. Meghanathan, Complex network analysis of the us marine highway network, in 20th ITNG (2023) , pp. 437–443
L.A. Neumann, E. Seraphim, O.A. Carpinteiro, E.M. Moreira, Participatory modeling: A new approach to model graph-oriented databases, in 19th ITNG (2022), pp. 97–106
A.Y. Ng, M.I. Jordan, Y. Weiss et al., On spectral clustering: Analysis and an algorithm. Adv. Neural Inf. Process. Syst. 2, 849–856 (2002)
A.T. Oliveira, A.D. Souza, E.M. Moreira, E. Seraphim, Mapping and conversion between relational and graph databases models: A systematic literature review, in 17th ITNG (2020), pp. 539–543
F. Pellegrini, A parallelisable multi-level banded diffusion scheme for computing balanced partitions with smooth boundaries, in European Conference on Parallel Processing (Springer, 2007), pp. 195–204
A. Pothen, H.D. Simon, K.P. Liou, Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Matrix Anal. Appl. 11(3), 430–452 (1990)
R. Sibson, Slink: an optimally efficient algorithm for the single-link cluster method. Comput. J. 16(1), 30–34 (1973)
D.A. Spielmat, S.H. Teng, Spectral partitioning works: Planar graphs and finite element meshes, in Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on (1996), pp. 96–105
U. Von Luxburg, A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)
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Siqueira, R.M.S., Alves, A.D., Carpinteiro, O.A.O., Moreira, E.M. (2024). Graph Partitioning Algorithms: A Comparative Study. In: Latifi, S. (eds) ITNG 2024: 21st International Conference on Information Technology-New Generations. ITNG 2024. Advances in Intelligent Systems and Computing, vol 1456. Springer, Cham. https://doi.org/10.1007/978-3-031-56599-1_65
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