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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2017.16
URN: urn:nbn:de:0030-drops-85494
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8549/
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Eppstein, David ; Kurz, Denis

K-Best Solutions of MSO Problems on Tree-Decomposable Graphs

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LIPIcs-IPEC-2017-16.pdf (0.5 MB)


Abstract

We show that, for any graph optimization problem in which the feasible solutions can be expressed by a formula in monadic second-order logic describing sets of vertices or edges and in which the goal is to minimize the sum of the weights in the selected sets, we can find the k best solution values for n-vertex graphs of bounded treewidth in time O(n + k log n). In particular, this applies to finding the k shortest simple paths between given vertices in directed graphs of bounded treewidth, giving an exponential speedup in the per-path cost over previous algorithms.

BibTeX - Entry

@InProceedings{eppstein_et_al:LIPIcs:2018:8549,
  author =	{David Eppstein and Denis Kurz},
  title =	{{K-Best Solutions of MSO Problems on Tree-Decomposable Graphs}},
  booktitle =	{12th International Symposium on Parameterized and Exact Computation (IPEC 2017)},
  pages =	{16:1--16:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-051-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{89},
  editor =	{Daniel Lokshtanov and Naomi Nishimura},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8549},
  URN =		{urn:nbn:de:0030-drops-85494},
  doi =		{10.4230/LIPIcs.IPEC.2017.16},
  annote =	{Keywords: graph algorithm, k-best, monadic second-order logic, treewidth}
}

Keywords: graph algorithm, k-best, monadic second-order logic, treewidth
Seminar: 12th International Symposium on Parameterized and Exact Computation (IPEC 2017)
Issue Date: 2018
Date of publication: 23.02.2018


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