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Assessing the Computational Complexity of Multi-layer Subgraph Detection

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Algorithms and Complexity (CIAC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10236))

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Abstract

Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the border of computational (in)tractability for the class of subgraph detection problems on multi-layer graphs, including fundamental problems such as maximum matching, finding certain clique relaxations (motivated by community detection), or path problems. Mostly encountering hardness results, sometimes even for two or three layers, we can also spot some islands of tractability.

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Notes

  1. 1.

    A preliminary full version containing all proofs is available at arXiv:1604.07724.

  2. 2.

    This actually describes the special case that the sets \(X_v\) from Theorem 1 all have size one.

References

  1. Agrawal, A., Lokshtanov, D., Mouawad, A.E., Saurabh, S.: Simultaneous feedback vertex set: a parameterized perspective. In: Proceedings of the 33rd International Symposium on Theoretical Aspects of Computer Science (STACS 2016). LIPIcs, vol. 47, pp. 7:1–7:15. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2016)

    Google Scholar 

  2. Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms and Applications, 2nd edn. Springer, London (2002)

    Book  MATH  Google Scholar 

  3. Berlingerio, M., Coscia, M., Giannotti, F., Monreale, A., Pedreschi, D.: Multidimensional networks: foundations of structural analysis. In: Proceedings of the 22nd International World Wide Web Conference (WWW 2013), vol. 16(5–6), pp. 567–593 (2013)

    Google Scholar 

  4. Boccaletti, S., Bianconi, G., Criado, R., del Genio, C.I., Gmez-Gardees, J., Romance, M., SendNadal, I., Wang, Z., Zanin, M.: The structure and dynamics of multilayer networks. Phys. Rep. 544(1), 1–122 (2014)

    Article  MathSciNet  Google Scholar 

  5. Boden, B., Günnemann, S., Hoffmann, H., Seidl, T.: Mining coherent subgraphs in multi-layer graphs with edge labels. In: The 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD 2012), pp. 1258–1266. ACM Press (2012)

    Google Scholar 

  6. Brandstädt, A., Le, V.B., Spinrad, J.P.: Graph Classes: A Survey. SIAM Monographs on Discrete Mathematics and Applications, vol. 3. SIAM, Philadelphia (1999)

    Book  MATH  Google Scholar 

  7. Bui-Xuan, B., Habib, M., Paul, C.: Competitive graph searches. Theor. Comput. Sci. 393(1–3), 72–80 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cai, L.: Fixed-parameter tractability of graph modification problems for hereditary properties. Inf. Process. Lett. 58(4), 171–176 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cai, L., Ye, J.: Dual connectedness of edge-bicolored graphs and beyond. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds.) MFCS 2014. LNCS, vol. 8635, pp. 141–152. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44465-8_13

    Google Scholar 

  10. Cohen, J.: Trusses: cohesive subgraphs for social network analysis. Technical report, National Security Agency, p. 16 (2008)

    Google Scholar 

  11. Cygan, M., Fomin, F.V., Kowalik, L., Lokshtanov, D., Marx, D., Pilipczuk, M., Pilipczuk, M., Saurabh, S.: Parameterized Algorithms. Springer, Cham (2015)

    Book  MATH  Google Scholar 

  12. Eppstein, D., Spiro, E.S.: The \(h\)-index of a graph and its application to dynamic subgraph statistics. J. Graph Algorithms Appl. 16(2), 543–567 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Fellows, M.R., Hermelin, D., Rosamond, F.A., Vialette, S.: On the parameterized complexity of multiple-interval graph problems. Theor. Comput. Sci. 410(1), 53–61 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Gai, A.T., Habib, M., Paul, C., Raffinot, M.: Identifying common connected components of graphs. Technical report, RR-LIRMM-03016, LIRMM, Université de Montpellier II (2003)

    Google Scholar 

  15. Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs, Annals of Discrete Mathematics, vol. 57, 2nd edn. Elsevier B. V., Amsterdam (2004)

    Google Scholar 

  16. Jiang, D., Pei, J.: Mining frequent cross-graph quasi-cliques. ACM Trans. Knowl. Discov. Data. 2(4), 16 (2009)

    Article  Google Scholar 

  17. Kano, M., Li, X.: Monochromatic and heterochromatic subgraphs in edge-colored graphs–a survey. Graphs Comb. 24(4), 237–263 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Khot, S., Raman, V.: Parameterized complexity of finding subgraphs with hereditary properties. Theor. Comput. Sci. 289(2), 997–1008 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  19. Kim, J., Lee, J.: Community detection in multi-layer graphs: a survey. SIGMOD Rec. 44(3), 37–48 (2015)

    Article  Google Scholar 

  20. Kivel, M., Arenas, A., Barthelemy, M., Gleeson, J.P., Moreno, Y., Porter, M.A.: Multilayer networks. J. Complex Netw. 2(3), 203–271 (2014)

    Article  Google Scholar 

  21. Lewis, J.M., Yannakakis, M.: The node-deletion problem for hereditary properties is NP-complete. J. Comput. Syst. Sci. 20(2), 219–230 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lin, B.: The parameterized complexity of \(k\)-biclique. In: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2015), pp. 605–615. SIAM (2015)

    Google Scholar 

  23. Monien, B.: How to find long paths efficiently. N.-Holl. Math. Stud. 109, 239–254 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  24. Mucha, P.J., Richardson, T., Macon, K., Porter, M.A., Onnela, J.P.: Community structure in time-dependent, multiscale, and multiplex networks. Science 328(5980), 876–878 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  25. Plummer, M.D.: Graph factors and factorization: 1985–2003: a survey. Discret. Math. 307(7–8), 791–821 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  26. Rossi, L., Musolesi, M., Torsello, A.: On the \(k\)-anonymization of time-varying and multi-layer social graphs. In: Proceedings of the 9th International Conference on Web and Social Media (ICWSM 2015), pp. 377–386. AAAI Press (2015)

    Google Scholar 

  27. Seidman, S.B.: Network structure and minimum degree. Soc. Netw. 5(3), 269–287 (1983)

    Article  MathSciNet  Google Scholar 

  28. Zeng, Z., Wang, J., Zhou, L., Karypis, G.: Out-of-core coherent closed quasi-clique mining from large dense graph databases. ACM Trans. Database Syst. 32(2), 13 (2007)

    Article  Google Scholar 

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Acknowledgment

HM and MS were supported by the DFG, project DAPA (NI 369/12). CK was supported by the DFG, project MAGZ (KO 3669/4–1). RB was partially supported by the DFG, fellowship BR 5207/2. This work was initiated at the research retreat of the TU Berlin Algorithmics and Computational Complexity group held in Darlingerode, Harz mountains, in April 2014.

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Authors and Affiliations

  1. Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany

    Robert Bredereck, Hendrik Molter, Rolf Niedermeier & Manuel Sorge

  2. Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany

    Christian Komusiewicz

  3. Institut für Informatik I, Universität Bonn, Bonn, Germany

    Stefan Kratsch

Authors
  1. Robert Bredereck
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  2. Christian Komusiewicz
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  3. Stefan Kratsch
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  4. Hendrik Molter
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  5. Rolf Niedermeier
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  6. Manuel Sorge
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Corresponding author

Correspondence to Hendrik Molter .

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Editors and Affiliations

  1. National Technical University of Athens, Zografou, Athens, Greece

    Dimitris Fotakis

  2. National Technical University of Athens, Zografou, Athens, Greece

    Aris Pagourtzis

  3. Université Paris-Dauphine, Paris, France

    Vangelis Th. Paschos

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Bredereck, R., Komusiewicz, C., Kratsch, S., Molter, H., Niedermeier, R., Sorge, M. (2017). Assessing the Computational Complexity of Multi-layer Subgraph Detection. In: Fotakis, D., Pagourtzis, A., Paschos, V. (eds) Algorithms and Complexity. CIAC 2017. Lecture Notes in Computer Science(), vol 10236. Springer, Cham. https://doi.org/10.1007/978-3-319-57586-5_12

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  • DOI: https://doi.org/10.1007/978-3-319-57586-5_12

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