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DOI: 10.4230/LIPIcs.IPEC.2017.27

An Output Sensitive Algorithm for Maximal Clique Enumeration in Sparse Graphs

Authors: George Manoussakis

Published in: LIPIcs, Volume 89, 12th International Symposium on Parameterized and Exact Computation (IPEC 2017)

Abstract

The degeneracy of a graph G is the smallest integer k such that every subgraph of G contains a vertex of degree at most k. Given an n-order k-degenerate graph G, we present an algorithm for enumerating all its maximal cliques. Assuming that c is the number of maximal cliques of G, our algorithm has setup time O(n(k^2+s(k+1))) and enumeration time cO((k+1)f(k+1)) where s(k+1) (resp. f(k+1)) is the preprocessing time (resp. enumeration time) for maximal clique enumeration in a general (k+1)-order graph. This is the first output sensitive algorithm whose enumeration time depends only on the degeneracy of the graph.

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George Manoussakis. An Output Sensitive Algorithm for Maximal Clique Enumeration in Sparse Graphs. In 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 89, pp. 27:1-27:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{manoussakis:LIPIcs.IPEC.2017.27,
  author =	{Manoussakis, George},
  title =	{{An Output Sensitive Algorithm for Maximal Clique Enumeration in Sparse Graphs}},
  booktitle =	{12th International Symposium on Parameterized and Exact Computation (IPEC 2017)},
  pages =	{27:1--27:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-051-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{89},
  editor =	{Lokshtanov, Daniel and Nishimura, Naomi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2017.27},
  URN =		{urn:nbn:de:0030-drops-85529},
  doi =		{10.4230/LIPIcs.IPEC.2017.27},
  annote =	{Keywords: enumeration algorithms, maximal cliques, k-degenerate graphs}
}

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DOI: 10.4230/LIPIcs.OPODIS.2016.11

Polynomial Self-Stabilizing Maximum Matching Algorithm with Approximation Ratio 2/3

Authors: Johanne Cohen, Khaled Maâmra, George Manoussakis, and Laurence Pilard

Published in: LIPIcs, Volume 70, 20th International Conference on Principles of Distributed Systems (OPODIS 2016)

Abstract

We present the first polynomial self-stabilizing algorithm for finding a (2/3)-approximation of a maximum matching in a general graph. The previous best known algorithm has been presented by Manne et al. and has a sub-exponential time complexity under the distributed adversarial daemon. Our new algorithm is an adaptation of the Manne et al. algorithm and works under the same daemon, but with a time complexity in O(n^3) moves. Moreover, our algorithm only needs one more boolean variable than the previous one, thus as in the Manne et al. algorithm, it only requires a constant amount of memory space (three identifiers and two booleans per node).

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Johanne Cohen, Khaled Maâmra, George Manoussakis, and Laurence Pilard. Polynomial Self-Stabilizing Maximum Matching Algorithm with Approximation Ratio 2/3. In 20th International Conference on Principles of Distributed Systems (OPODIS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 70, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{cohen_et_al:LIPIcs.OPODIS.2016.11,
  author =	{Cohen, Johanne and Ma\^{a}mra, Khaled and Manoussakis, George and Pilard, Laurence},
  title =	{{Polynomial Self-Stabilizing Maximum Matching Algorithm with Approximation Ratio 2/3}},
  booktitle =	{20th International Conference on Principles of Distributed Systems (OPODIS 2016)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-031-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{70},
  editor =	{Fatourou, Panagiota and Jim\'{e}nez, Ernesto and Pedone, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2016.11},
  URN =		{urn:nbn:de:0030-drops-70808},
  doi =		{10.4230/LIPIcs.OPODIS.2016.11},
  annote =	{Keywords: Self-Stabilization, Distributed Algorithm, Fault Tolerance, Matching}
}

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Documents authored by Manoussakis, George

An Output Sensitive Algorithm for Maximal Clique Enumeration in Sparse Graphs

Abstract

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Polynomial Self-Stabilizing Maximum Matching Algorithm with Approximation Ratio 2/3

Abstract

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