Complexity Aspects of Unstructured Sparse Graph Representation
Article No.: 26, Pages 1 - 3
Abstract
In this paper, we address the problem of the trade-off between the compact memory representation of graphs and their amount of randomness. We design a representation (abbreviated as DBP representation) which does not use information on the structure of graphs, hence it is generally usable. Based on our theoretical lower bound on graph space representation, we define a compression ratio for a given graph with respect to the DBP representation. Based on experimental results, we derive the empirical relationship between the amount of randomness and the compression ratio.
References
[1]
P. Bartalos: Effective Encoding and the Kolmogorov Complexity of the Internet. In Proc. of the Student Research Confernece, IIT.SRC 2006, SUT Publishing, Bratislava, pp. 121--128 (2006)
[2]
M. Bastian, S. Heymann, M. Jacomy: Gephi: an open source software for exploring and manipulating networks. In Proc. of the 3rd Int. AAAI Conference on Weblogs and Social media, ICWSM 2009, The AAAI Press, pp. 361--362 (2009)
[3]
D. K. Blandford, G. E. Blelloch, I. A. Kash: Compact representations of separable graphs. In Proc. of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2003, The ACM/SIAM Press, pp. 679--688 (2003)
[4]
G. E. Blelloch, A. Farzan: Succinct Representations of Separable Graphs. In Proc. of the 21st Annual Symposium on Combinatorial Pattern Matching, CPM 2010, Springer, LNCS 6129, pp. 138--150 (2010)
[5]
P. Boldi, S. Vigna: (Web/Social) Graph Compression. Encyclopedia of Big Data Technologies (S. Sakr and A. Y. Zomaya eds.), Springer, pp. 1800--1804 (2019)
[6]
P. Boldi, S. Vigna: The webgraph framework I: compression techniques. In Proc. of the 13th Int. Conference on World Wide Web, WWW 2004, ACM Press, pp. 595--602 (2004)
[7]
T. Bu, D. F. Towsley: On Distinguishing between Internet Power Law Topology Generators. In Proc. of the 21st Annual Joint Conference of the IEEE Computer and Communications Societies INFOCOM 2002, pp. 638--647 (2002)
[8]
F. Claude, G. Navarro: Fast and Compact Web Graph Representations. ACM Transactions on The Web, 4(4), pp. 16:1-16:31 (2010)
[9]
A. Farzan, J. I. Munro: Succinct encoding of arbitrary graphs, Theor. Comput. Science, 513, pp. 38--52 (2013)
[10]
S. á. García: Compact and Efficient Representations of Graphs. PhD Thesis, Departamento de Computación, Facultad de Informática, Universidade da Coruña (2014)
[11]
Inet Topology Generator. Download Web-page, URL: http://topology.eecs.umich.edu/inet/
[12]
S. Janson, T. Luczak, A. Rucinski: Random Graphs. John Wiley & Sons, New York (2000)
[13]
M. Li, P. Vitányi: An introduction to Kolmogorov complexity and its applications (2nd ed.). Springer-Verlag New York, Inc., Secaucus, NJ, USA (1997)
[14]
C. C. McGeoch: A Guide to Experimental Algorithmics. Cambridge University Press, New York (2012)
[15]
M. Nehéz, P. Bartalos: On Space Complexity of Sparse Graphs Representation. In Proc. of the 6th Conference on Applied Mathematics, APLIMAT 2007, Dept. of Mathematics, Faculty of Mechanical Engineering, SUT, Bratislava, Part III, pp. 219--226 (2007)
[16]
E. M. Palmer: Graphical Evolution. John Wiley & Sons, Inc., New York (1985)
[17]
S. Raghavan, H. Garcia-Molina: Representing Web Graphs. In Proc. of the 19th Int. Conference on Data Engineering, ICDE 2003, IEEE Computer Society, pp. 405--416 (2003)
[18]
R. Raman, V. Raman, S. Rao Satti: Succinct Indexable Dictionaries with Applications to Encoding k-ary Trees, Prefix Sums and Multisets. ACM Transactions on Algorithms, 3(4), pp. 43:1-43:25 (2007)
[19]
H. J. Rogers (Jr.).: Theory of Recursive Functions and Effective Computability. MIT Press (1987)
[20]
T. Suel, J. Yuan: Compressing the Graph Structure of the Web, Data Compression Conference, DCC 2001, IEEE Computer Society, pp. 213--222 (2001)
[21]
H. Zenil, N. A. Kiani, J. Tegner: Methods of information theory and algorithmic complexity for network biology. Seminars in Cell & Developmental Biology, 51, pp. 32--43 (2016)
- Complexity Aspects of Unstructured Sparse Graph Representation
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Published In
September 2019
225 pages
ISBN:9781450371933
DOI:10.1145/3351556
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Published: 26 September 2019
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BCI'19 Paper Acceptance Rate 24 of 73 submissions, 33%;
Overall Acceptance Rate 97 of 250 submissions, 39%
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