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PACE Solver Description

DOI: 10.4230/LIPIcs.IPEC.2023.39

PACE Solver Description: Zygosity

Authors: Emmanuel Arrighi, Pål Grønås Drange, Kenneth Langedal, Farhad Vadiee, Martin Vatshelle, and Petra Wolf

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract

The graph parameter twin-width was recently introduced by Bonnet et al. Twin-width is a parameter that measures a graph’s similarity to a cograph, which is a graph that can be reduced to a single vertex by repeatedly contracting twins. This brief description introduces Zygosity, a heuristic for computing a low-width contraction sequence that achieved second place in the 2023 edition of Parameterized Algorithms and Computational Experiments Challenge (PACE). Zygosity starts by repeatedly contracting twins. Then, any attached trees are contracted down to a single pendant vertex. The remaining graph is then contracted using a randomized greedy algorithm.

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Emmanuel Arrighi, Pål Grønås Drange, Kenneth Langedal, Farhad Vadiee, Martin Vatshelle, and Petra Wolf. PACE Solver Description: Zygosity. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 39:1-39:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{arrighi_et_al:LIPIcs.IPEC.2023.39,
  author =	{Arrighi, Emmanuel and Drange, P\r{a}l Gr{\o}n\r{a}s and Langedal, Kenneth and Vadiee, Farhad and Vatshelle, Martin and Wolf, Petra},
  title =	{{PACE Solver Description: Zygosity}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{39:1--39:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.39},
  URN =		{urn:nbn:de:0030-drops-194583},
  doi =		{10.4230/LIPIcs.IPEC.2023.39},
  annote =	{Keywords: Twin-width, randomized greedy algorithm}
}

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DOI: 10.4230/LIPIcs.SEA.2022.12

Efficient Minimum Weight Vertex Cover Heuristics Using Graph Neural Networks

Authors: Kenneth Langedal, Johannes Langguth, Fredrik Manne, and Daniel Thilo Schroeder

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract

Minimum weighted vertex cover is the NP-hard graph problem of choosing a subset of vertices incident to all edges such that the sum of the weights of the chosen vertices is minimum. Previous efforts for solving this in practice have typically been based on search-based iterative heuristics or exact algorithms that rely on reduction rules and branching techniques. Although exact methods have shown success in solving instances with up to millions of vertices efficiently, they are limited in practice due to the NP-hardness of the problem. We present a new hybrid method that combines elements from exact methods, iterative search, and graph neural networks (GNNs). More specifically, we first compute a greedy solution using reduction rules whenever possible. If no such rule applies, we consult a GNN model that selects a vertex that is likely to be in or out of the solution, potentially opening up for further reductions. Finally, we use an improved local search strategy to enhance the solution further. Extensive experiments on graphs of up to a billion edges show that the proposed GNN-based approach finds better solutions than existing heuristics. Compared to exact solvers, the method produced solutions that are, on average, 0.04% away from the optimum while taking less time than all state-of-the-art alternatives.

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Kenneth Langedal, Johannes Langguth, Fredrik Manne, and Daniel Thilo Schroeder. Efficient Minimum Weight Vertex Cover Heuristics Using Graph Neural Networks. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{langedal_et_al:LIPIcs.SEA.2022.12,
  author =	{Langedal, Kenneth and Langguth, Johannes and Manne, Fredrik and Schroeder, Daniel Thilo},
  title =	{{Efficient Minimum Weight Vertex Cover Heuristics Using Graph Neural Networks}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.12},
  URN =		{urn:nbn:de:0030-drops-165462},
  doi =		{10.4230/LIPIcs.SEA.2022.12},
  annote =	{Keywords: Minimum weighted vertex cover, Maximum weighted independent set, Graph neural networks, Reducing-peeling}
}

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Documents authored by Langedal, Kenneth

PACE Solver Description: Zygosity

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Efficient Minimum Weight Vertex Cover Heuristics Using Graph Neural Networks

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