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DOI: 10.4230/LIPIcs.MFCS.2024.60

On the Complexity of Community-Aware Network Sparsification

Authors: Emanuel Herrendorf, Christian Komusiewicz, Nils Morawietz, and Frank Sommer

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract

In the NP-hard Π-Network Sparsification problem, we are given an edge-weighted graph G, a collection 𝒞 of c subsets of V(G), called communities, and two numbers 𝓁 and b, and the question is whether there exists a spanning subgraph G' of G with at most 𝓁 edges of total weight at most b such that G'[C] fulfills Π for each community C ∈ 𝒞. We study the fine-grained and parameterized complexity of two special cases of this problem: Connectivity NWS where Π is the connectivity property and Stars NWS, where Π is the property of having a spanning star. First, we provide a tight 2^Ω(n²+c)-time running time lower bound based on the ETH for both problems, where n is the number of vertices in G even if all communities have size at most 4, G is a clique, and every edge has unit weight. For the connectivity property, the unit weight case with G being a clique is the well-studied problem of computing a hypergraph support with a minimum number of edges. We then study the complexity of both problems parameterized by the feedback edge number t of the solution graph G'. For Stars NWS, we present an XP-algorithm for t answering an open question by Korach and Stern [Discret. Appl. Math. '08] who asked for the existence of polynomial-time algorithms for t = 0. In contrast, we show for Connectivity NWS that known polynomial-time algorithms for t = 0 [Korach and Stern, Math. Program. '03; Klemz et al., SWAT '14] cannot be extended to larger values of t by showing NP-hardness for t = 1.

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Emanuel Herrendorf, Christian Komusiewicz, Nils Morawietz, and Frank Sommer. On the Complexity of Community-Aware Network Sparsification. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 60:1-60:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{herrendorf_et_al:LIPIcs.MFCS.2024.60,
  author =	{Herrendorf, Emanuel and Komusiewicz, Christian and Morawietz, Nils and Sommer, Frank},
  title =	{{On the Complexity of Community-Aware Network Sparsification}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{60:1--60:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.60},
  URN =		{urn:nbn:de:0030-drops-206169},
  doi =		{10.4230/LIPIcs.MFCS.2024.60},
  annote =	{Keywords: parameterized complexity, hypergraph support, above guarantee parameterization, exponential-time-hypothesis}
}

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PACE Solver Description

DOI: 10.4230/LIPIcs.IPEC.2021.28

PACE Solver Description: ADE-Solver

Authors: Alexander Bille, Dominik Brandenstein, and Emanuel Herrendorf

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract

This document describes our exact solver "ADE" for the unweighted cluster editing problem submitted to the PACE 2021 competition. The solver’s core consists of an FPT-algorithm using a branch and bound strategy in conjunction with several data reduction rules.

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Alexander Bille, Dominik Brandenstein, and Emanuel Herrendorf. PACE Solver Description: ADE-Solver. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 28:1-28:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bille_et_al:LIPIcs.IPEC.2021.28,
  author =	{Bille, Alexander and Brandenstein, Dominik and Herrendorf, Emanuel},
  title =	{{PACE Solver Description: ADE-Solver}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{28:1--28:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.28},
  URN =		{urn:nbn:de:0030-drops-154112},
  doi =		{10.4230/LIPIcs.IPEC.2021.28},
  annote =	{Keywords: Unweighted Cluster Editing}
}

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On the Complexity of Community-Aware Network Sparsification

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PACE Solver Description: ADE-Solver

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