License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2019.3
URN: urn:nbn:de:0030-drops-114990
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11499/
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Haraguchi, Kazuya ; Nagamochi, Hiroshi

A Polynomial-Delay Algorithm for Enumerating Connectors Under Various Connectivity Conditions

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LIPIcs-ISAAC-2019-3.pdf (0.6 MB)

Abstract

We are given an instance (G,I,sigma) with a graph G=(V,E), a set I of items, and a function sigma:V -> 2^I. For a subset X of V, let G[X] denote the subgraph induced from G by X, and I_sigma(X) denote the common item set over X. A subset X of V such that G[X] is connected is called a connector if, for any vertex v in V\X, G[X cup {v}] is not connected or I_sigma(X cup {v}) is a proper subset of I_sigma(X).
In this paper, we present the first polynomial-delay algorithm for enumerating all connectors. For this, we first extend the problem of enumerating connectors to a general setting so that the connectivity condition on X in G can be specified in a more flexible way. We next design a new algorithm for enumerating all solutions in the general setting, which leads to a polynomial-delay algorithm for enumerating all connectors for several connectivity conditions on X in G, such as the biconnectivity of G[X] or the k-edge-connectivity among vertices in X in G.

BibTeX - Entry

@InProceedings{haraguchi_et_al:LIPIcs:2019:11499,
  author =	{Kazuya Haraguchi and Hiroshi Nagamochi},
  title =	{{A Polynomial-Delay Algorithm for Enumerating Connectors Under Various Connectivity Conditions}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11499},
  URN =		{urn:nbn:de:0030-drops-114990},
  doi =		{10.4230/LIPIcs.ISAAC.2019.3},
  annote =	{Keywords: Graph with itemsets, Enumeration, Polynomial-delay algorithms, Connectors}
}

Keywords: Graph with itemsets, Enumeration, Polynomial-delay algorithms, Connectors
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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