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Isolation concepts applied to temporal clique enumeration

Published online by Cambridge University Press:  16 October 2020

Hendrik Molter Open the ORCID record for Hendrik Molter [Opens in a new window] ,
Rolf Niedermeier  and
Malte Renken
Hendrik Molter*
Affiliation:
TU Berlin, Faculty IV, Algorithmics and Computational Complexity (emails: rolf.niedermeier@tu-berlin.de, m.renken@tu-berlin.de)
Rolf Niedermeier
Affiliation:
TU Berlin, Faculty IV, Algorithmics and Computational Complexity (emails: rolf.niedermeier@tu-berlin.de, m.renken@tu-berlin.de)
Malte Renken
Affiliation:
TU Berlin, Faculty IV, Algorithmics and Computational Complexity (emails: rolf.niedermeier@tu-berlin.de, m.renken@tu-berlin.de)
*
*Corresponding author. Email: h.molter@tu-berlin.de
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Abstract

Isolation is a concept originally conceived in the context of clique enumeration in static networks, mostly used to model communities that do not have much contact to the outside world. Herein, a clique is considered isolated if it has few edges connecting it to the rest of the graph. Motivated by recent work on enumerating cliques in temporal networks, we transform the isolation concept to the temporal setting. We discover that the addition of the time dimension leads to six distinct natural isolation concepts. Our main contribution is the development of parameterized enumeration algorithms for five of these six isolation types for clique enumeration, employing the parameter “degree of isolation.” In a nutshell, this means that the more isolated these cliques are, the faster we can find them. On the empirical side, we implemented and tested these algorithms on (temporal) social network data, obtaining encouraging results.

Keywords

community detectiondense subgraphssocial network analysistime-evolving dataenumeration algorithmsfixed-parameter tractability
Type
Research Article
Information
Network Science , Volume 9 , Special Issue S1: Complex Networks 2019 , October 2021 , pp. S83 - S105
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

Special Issue Editor: Hocine Cherifi

*

An extended abstract of this work appeared under the title “Enumerating Isolated Cliques in Temporal Networks” in the proceedings of the 8th International Conference on Complex Networks and their Applications (Molter et al., 2019). This version contains full proof details and a comprehensive empirical evaluation. This work was supported by the DFG, project MATE (NI 369/17).

References

Bentert, M., Himmel, A.-S., Molter, H., Morik, M., Niedermeier, R., & Saitenmacher, R. (2019). Listing All Maximal k-Plexes in Temporal Graphs. ACM Journal of Experimental Algorithmics, 24(1), 1.13:1–1.13:27.CrossRefGoogle Scholar
van Bevern, R., Fluschnik, T., Mertzios, G.B., Molter, H., Sorge, M., & Suchý, O. (2018). The parameterized complexity of finding secluded solutions to some classical optimization problems on graphs. Discrete Optimization, 30, 20–50.CrossRefGoogle Scholar
Chechik, S., Johnson, M.P., Parter, M., & Peleg, D. (2017). Secluded connectivity problems. Algorithmica, 79(3), 708–741.CrossRefGoogle Scholar
Cygan, M., Fomin, F.V., Kowalik, Ł., Lokshtanov, D., Marx, D., Pilipczuk, M., Pilipczuk, M. & Saurabh, S. (2015). Parameterized algorithms. Springer.CrossRefGoogle Scholar
Downey, R.G., & Fellows, M.R. (2013). Fundamentals of parameterized complexity. Springer.CrossRefGoogle Scholar
Eppstein, D., & Strash, D. (2013). Listing all maximal cliques in large sparse real-world graphs. ACM Journal of Experimental Algorithmics, 18, 3.1:1–3.1:21.Google Scholar
Flum, J., & Grohe, M. (2006). Parameterized complexity theory. Texts in Theoretical Computer Science. An EATCS Series, vol. XIV. Springer.Google Scholar
Fomin, F.V., Golovach, P.A., Karpov, N., & Kulikov, A.S. (2017). Parameterized complexity of secluded connectivity problems. Theory of Computing Systems, 61(3), 795–819.CrossRefGoogle Scholar
Fournet, J., & Barrat, A. (2014). Contact patterns among high school students. PLOS ONE, 9(9), 1–17.CrossRefGoogle Scholar
Gemmetto, V., Barrat, A., & Cattuto, C. (2014). Mitigation of infectious disease at school: Targeted class closure vs school closure. BMC Infectious Diseases, 14(1), 695.CrossRefGoogle Scholar
Génois, M, & Barrat, A. (2018). Can co-location be used as a proxy for face-to-face contacts? EPJ Data Science, 7(1), 11.CrossRefGoogle Scholar
Golovach, P.A., Heggernes, P., Lima, P.T., & Montealegre, P. (2020). Finding connected secluded subgraphs. Journal of Computer and System Sciences, 113, 101–124.CrossRefGoogle Scholar
Himmel, A.-S., Molter, H., Niedermeier, R., & Sorge, M. (2017). Adapting the Bron-Kerbosch algorithm for enumerating maximal cliques in temporal graphs. Social Network Analysis and Mining, 7(1), 35:1–35:16.Google Scholar
Holme, P., & Saramäki, J. (2019). Temporal network theory. Springer.CrossRefGoogle Scholar
Håstad, J. (1999). Clique is hard to approximate within n 1–ε. Acta Mathematica, 182(1), 105–142.CrossRefGoogle Scholar
Hüffner, F., Komusiewicz, C., Moser, H., & Niedermeier, R. (2009). Isolation concepts for clique enumeration: Comparison and computational experiments. Theoretical computer science, 410(52), 5384–5397.CrossRefGoogle Scholar
Ito, H., & Iwama, K. (2009). Enumeration of isolated cliques and pseudo-cliques. ACM Transactions on Algorithms, 5(4), 40:1–40:21.Google Scholar
Karp, R.M. (1972). Reducibility among combinatorial problems. In Complexity of computer computations (pp. 85–103). Springer.CrossRefGoogle Scholar
Komusiewicz, C., Hüffner, F., Moser, H., & Niedermeier, R. (2009). Isolation concepts for efficiently enumerating dense subgraphs. Theoretical Computer Science, 410(38-40), 3640–3654.CrossRefGoogle Scholar
Latapy, M., Viard, T., & Magnien, C. (2018). Stream graphs and link streams for the modeling of interactions over time. Social Network Analysis and Mining, 8(1), 61:1–61:29.Google Scholar
Michail, O. (2016). An introduction to temporal graphs: An algorithmic perspective. Internet Mathematics, 12(4), 239–280.CrossRefGoogle Scholar
Molter, H., Niedermeier, R., & Renken, M. (2019). Enumerating isolated cliques in temporal networks. Proceedings of the 8th international conference on complex networks and their applications (pp. 519–531). SCI, vol. 882. Springer.Google Scholar
Niedermeier, R. (2006). Invitation to fixed-parameter algorithms. Oxford University Press.CrossRefGoogle Scholar
Rossetti, G., & Cazabet, R. (2018). Community discovery in dynamic networks: a survey. ACM Computing Surveys, 51(2), 1–37.CrossRefGoogle Scholar
Stehlé, J., Voirin, N., Barrat, A., Cattuto, C., Isella, L., Pinton, J.-F., Quaggiotto, M., Van den Broeck, W., Régis, C., Lina, B., et al.. (2011). High-resolution measurements of face-to-face contact patterns in a primary school. PLOS ONE, 6(8).CrossRefGoogle Scholar
Tomita, E., Tanaka, A., & Takahashi, H. (2006). The worst-case time complexity for generating all maximal cliques and computational experiments. Theoretical Computer Science, 363(1), 28–42.CrossRefGoogle Scholar
Viard, T., Latapy, M., & Magnien, C. (2016). Computing maximal cliques in link streams. Theoretical Computer Science, 609, 245–252.CrossRefGoogle Scholar
Viard, T., Magnien, C., & Latapy, M. (2018). Enumerating maximal cliques in link streams with durations. Information Processing Letters, 133, 44–48.CrossRefGoogle Scholar