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Speeding up Networks Mining via Neighborhood Diversity

Authors Gennaro Cordasco , Luisa Gargano , Adele A. Rescigno

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Author Details

Gennaro Cordasco
  • Dipartimento di Psicologia, Università della Campania "Luigi Vanvitelli", Caserta, Italy
Luisa Gargano
  • Dipartimento di Informatica, Università di Salerno, Fisciano, Italy
Adele A. Rescigno
  • Dipartimento di Informatica, Università di Salerno, Fisciano, Italy

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Gennaro Cordasco, Luisa Gargano, and Adele A. Rescigno. Speeding up Networks Mining via Neighborhood Diversity. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 21:1-21:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.FUN.2021.21

Abstract

Parameterized complexity was classically used to efficiently solve NP-hard problems for small values of a fixed parameter. Then it has also been used as a tool to speed up algorithms for tractable problems. Following this line of research, we design algorithms parameterized by neighborhood diversity (nd) for several graph theoretic problems in P (e.g., Maximum Matching, Triangle counting and listing, Girth and Global minimum vertex cut). Such problems are known to admit algorithms parameterized by modular-width (mw) and consequently - being the nd a "special case" of mw - by nd. However, the proposed novel algorithms allow to improve the computational complexity from a time O(f(mw)⋅ n +m) - where n and m denote, respectively, the number of vertices and edges in the input graph - which is multiplicative in n to a time O(g(nd)+n +m) which is additive only in the size of the input.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Parameterized Complexity
  • Neighborhood Diversity
  • Maximum Matching
  • Triangle Counting
  • Girth
  • Global minimum vertex cut

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References

  1. A. Abboud, F. Grandoni, and V. V. Williams. Subcubic equivalences between graph centrality problems, apsp and diameter. In ACM-SIAM Symposium on Discrete Algorithms (SODA), 1681-1697, 2015. Google Scholar
  2. A. Abboud and V. V. Williams. Popular conjectures imply strong lower bounds for dynamic problems. In IEEE Symposium on Foundations of Computer Science (FOCS'14). IEEE, 434-443, 2014. Google Scholar
  3. F. N. Abu-Khzam, S. Li, C. Markarian, F. Meyer auf der Heide, and P. Podlipyan. Modular-Width: An Auxiliary Parameter for Parameterized Parallel Complexity. In Frontiers in Algorithmics, FAW 2017, LNCS 10336, 2017. Google Scholar
  4. N. Alon, R. Yuster, and U. Zwick. Finding and counting given length cycles. Algorithmica, 17(3): 209-223, 1997. Google Scholar
  5. S. E. Asch. Studies of independence and conformity: A minority of one against a unanimous majority. Psychological Monographs, 70, 1956. Google Scholar
  6. L. Becchetti, P. Boldi, C. Castillo, and A. Gionis. Efficient algorithms for large-scale local triangle counting. ACM Trans. Knowl. Discov. Data 4 (3), 2010. Google Scholar
  7. R. Belmonte, F. V. Fomin, P. A. Golovach, and M. S. Ramanujan. Metric Dimension of Bounded Width Graphs. Mathematical Foundations of Computer Science (MFCS '15), LNCS 923, 2015. Google Scholar
  8. M. Bentert, T. Fluschnik, A. Nichterlein, and R. Niedermeier. Parameterized aspects of triangle enumeration. Journal of Computer and System Sciences, 103, 61-77, 2019. Google Scholar
  9. M. Borassi, P. Crescenzi, and M. Habib. Into the square: On the complexity of some quadratic-time solvable problems. Electronic Notes in Theoretical Computer Science, 322:51-67, 2016. Google Scholar
  10. G. Cordasco, L. Gargano, A. A. Rescigno, and U. Vaccaro. Optimizing spread of influence in social networks via partial incentives. In 22nd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2015. LNCS 9439, 119-134, 2015. Google Scholar
  11. G. Cordasco, L. Gargano, A. A. Rescigno, and U. Vaccaro. Evangelism in social networks: Algorithms and complexity. Networks 71(4): 346-357, 2018. Google Scholar
  12. D. Coudert, G. Ducoffe, and A. Popa. Fully polynomial FPT algorithms for some classes of bounded clique-width graphs. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '18), 2765-2784, 2018. Google Scholar
  13. M. Doucha and J. Kratochvíl. Cluster Vertex Deletion: A Parameterization between Vertex Cover and Clique-Width. MFCS 2012, 348-359, 2012. Google Scholar
  14. R. G. Downey and M. R. Fellows. Parameterized Complexity. Springer, 2012. Google Scholar
  15. P. Dvorák, D. Knop, and T. Toufar. Target Set Selection in Dense Graph Classes. In arXiv:1610.07530, 2016. Google Scholar
  16. D. Easley and J. Kleinberg. Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press, ISBN:0521195330, 2010. Google Scholar
  17. J. Edmonds. Paths, trees, and flowers. Canadian Journal of mathematics, 17(3):449-467, 1965. Google Scholar
  18. J. Fiala, T. Gavenciak, D. Knop, M. Koutecky, and J. Kratochvíl. Fixed parameter complexity of distance constrained labeling and uniform channel assignment problems. In arXiv:1507.00640, 2015. Google Scholar
  19. F. V. Fomin, M. Liedloff, P. Montealegre, and I. Todinca. Algorithms Parameterized by Vertex Cover and Modular Width, through Potential Maximal Cliques. In Ravi R., Gørtz I.L. (eds) Algorithm Theory – SWAT 2014, LNCS vol 8503, Springer, 2014. Google Scholar
  20. H. N. Gabow. Data structures for weighted matching and extensions to b-matching and f-factors. ACM Transactions on Algorithms, Vol. 14 (3), Article 39, 2018. Google Scholar
  21. J. Gajarský, M. Lampis, and S. Ordyniak. Parameterized Algorithms for Modular-Width. In Gutin G., Szeider S. (eds) Parameterized and Exact Computation, IPEC 2013, LNCS 8246, 2013. Google Scholar
  22. A. Gajentaan and M. H. Overmars. On a class of o(n²) problems in computational geometry. Computational Geometry, 5(3):165-185, 1995. Google Scholar
  23. F. Le Gall. Powers of tensors and fast matrix multiplication. In Proceedings of the 39th International Symposium on Symbolic and Algebraic ComputationJuly, ISSAC '14, 296-303, 2014. Google Scholar
  24. R. Ganian. Using neighborhood diversity to solve hard problems. In arXiv:1201.3091, 2012. Google Scholar
  25. L. Gargano and A.A. Rescigno. Complexity of conflict-free colorings of graphs. Theoretical Computer Science, 566, 39-49, 2015. Google Scholar
  26. A. C. Giannopoulou, G. B. Mertzios, and R. Niedermeier. Polynomial fixed-parameter algorithms: A case study for longest path on interval graphs. Theoretical Computer Science, 689: 67-95, 2017. Google Scholar
  27. J. Hao and J. B. Orlin. A faster algorithm for finding the minimum cut in a directed graph. J. Algorithms, 17(3):424-446, 1994. Google Scholar
  28. A. Itai and M. Rodeh. Finding a minimum circuit in a graph. SIAM Journal on Computing, 7(4):413-423, 1978. Google Scholar
  29. M. N. Kolountzakis, G. L. Miller, R. Peng, and C. E. Tsourakakis. Efficient triangle counting in large graphs via degree-based vertex partitioning. Internet Math. 8 (1-2), 161-185, 2012. Google Scholar
  30. D. Kratsch and J. P. Spinrad. Between o(nm) and o(n^α). SIAM Journal on Computing, 36(2):310-325, 2006. Google Scholar
  31. S. Kratsch and F. Nelles. Efficient and adaptive parameterized algorithms on modular decompositions. In arXiv:1804.10173, 2018. Google Scholar
  32. M. Lampis. Algorithmic meta-theorems for restrictions of treewidth. Algorithmica 64, 19-37, 2012. Google Scholar
  33. G. B. Mertzios, A. Nichterlein, , and R. Niedermeier. The power of linear-time data reduction for maximum matching. In Proceedings of the International Symposium on Mathematical Foundations of Computer Science (MFCS'17), 83, 46:1-46:14, 2017. Google Scholar
  34. S. Micali and V. V. Vazirani. An o(sqrt(|V|) |E|) algorithm for finding maximum matching in general graphs. In 21st Annual Symposium on Foundations of Computer Science, 17-27, 1980. Google Scholar
  35. M. E. J. Newman. The structure and function of complex networks. SIAM Rev. 45 (2), 167-256, 2003. Google Scholar
  36. R. Niedermeier. Invitation to Fixed-Parameter Algorithms. Oxford University Press, 2006. Google Scholar
  37. V. V. Williams. Hardness of easy problems: Basing hardness on popular conjectures such as the strong exponential time hypothesis (invited talk). In International Symposium on Parameterized and Exact Computation (IPEC), 16-28, 2015. Google Scholar
  38. V. V. Williams and R. R. Williams. Subcubic equivalences between path, matrix and triangle problems. In IEEE Symposium on Foundations of Computer Science (FOCS), 645-654, 2010. Google Scholar
  39. Y. Zhang and S. Parthasarathy. Extracting analyzing and visualizing triangle k-core motifs within networks. In Proceedings of the 28th International Conference on Data Engineering, ICDE '12, IEEE Computer Society, 1049-1060, 2012. Google Scholar
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