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DOI: 10.4230/LIPIcs.ISAAC.2017.36

On Structural Parameterizations of the Edge Disjoint Paths Problem

Authors: Robert Ganian, Sebastian Ordyniak, and Ramanujan Sridharan

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract

In this paper we revisit the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal pair in P. Our focus lies on structural parameterizations for the problem that allow for efficient (polynomial-time or fpt) algorithms. As our first result, we answer an open question stated in Fleszar, Mnich, and Spoerhase (2016), by showing that the problem can be solved in polynomial time if the input graph has a feedback vertex set of size one. We also show that EDP parameterized by the treewidth and the maximum degree of the input graph is fixed-parameter tractable. Having developed two novel algorithms for EDP using structural restrictions on the input graph, we then turn our attention towards the augmented graph, i.e., the graph obtained from the input graph after adding one edge between every terminal pair. In constrast to the input graph, where EDP is known to remain NP-hard even for treewidth two, a result by Zhou et al. (2000) shows that EDP can be solved in non-uniform polynomial time if the augmented graph has constant treewidth; we note that the possible improvement of this result to an fpt-algorithm has remained open since then. We show that this is highly unlikely by establishing the W[1]-hardness of the problem parameterized by the treewidth (and even feedback vertex set) of the augmented graph. Finally, we develop an fpt-algorithm for EDP by exploiting a novel structural parameter of the augmented graph.

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Robert Ganian, Sebastian Ordyniak, and Ramanujan Sridharan. On Structural Parameterizations of the Edge Disjoint Paths Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{ganian_et_al:LIPIcs.ISAAC.2017.36,
  author =	{Ganian, Robert and Ordyniak, Sebastian and Sridharan, Ramanujan},
  title =	{{On Structural Parameterizations of the Edge Disjoint Paths Problem}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{36:1--36:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.36},
  URN =		{urn:nbn:de:0030-drops-82555},
  doi =		{10.4230/LIPIcs.ISAAC.2017.36},
  annote =	{Keywords: edge disjoint path problem, feedback vertex set, treewidth, fracture number, parameterized complexity}
}

Document

DOI: 10.4230/LIPIcs.IPEC.2016.23

Backdoors for Linear Temporal Logic

Authors: Arne Meier, Sebastian Ordyniak, Ramanujan Sridharan, and Irena Schindler

Published in: LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

Abstract

In the present paper, we introduce the backdoor set approach into the field of temporal logic for the global fragment of linear temporal logic. We study the parameterized complexity of the satisfiability problem parameterized by the size of the backdoor. We distinguish between backdoor detection and evaluation of backdoors into the fragments of Horn and Krom formulas. Here we classify the operator fragments of globally-operators for past/future/always, and the combination of them. Detection is shown to be fixed-parameter tractable (FPT) whereas the complexity of evaluation behaves differently. We show that for Krom formulas the problem is paraNP-complete. For Horn formulas, the complexity is shown to be either fixed parameter tractable or paraNP-complete depending on the considered operator fragment.

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Arne Meier, Sebastian Ordyniak, Ramanujan Sridharan, and Irena Schindler. Backdoors for Linear Temporal Logic. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{meier_et_al:LIPIcs.IPEC.2016.23,
  author =	{Meier, Arne and Ordyniak, Sebastian and Sridharan, Ramanujan and Schindler, Irena},
  title =	{{Backdoors for Linear Temporal Logic}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{23:1--23:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Guo, Jiong and Hermelin, Danny},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.23},
  URN =		{urn:nbn:de:0030-drops-69462},
  doi =		{10.4230/LIPIcs.IPEC.2016.23},
  annote =	{Keywords: Linear Temporal Logic, Parameterized Complexity, Backdoor Sets}
}

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Documents authored by Sridharan, Ramanujan

On Structural Parameterizations of the Edge Disjoint Paths Problem

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Backdoors for Linear Temporal Logic

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