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.SWAT.2016.32
URN: urn:nbn:de:0030-drops-60535
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6053/
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Marx, Dániel

The Complexity Landscape of Fixed-Parameter Directed Steiner Network Problems (Invited Talk)

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LIPIcs-SWAT-2016-32.pdf (0.2 MB)

Abstract

Given a directed graph G and a list (s_1,t_1), ..., (s_k,t_k) of terminal pairs, the Directed Steiner Network problem asks for a minimum-cost subgraph of G that contains a directed s_i-> t_i path for every 1<= i <= k. Feldman and Ruhl presented an n^{O(k)} time algorithm for the problem, which shows that it is polynomial-time solvable for every fixed number k of demands. There are special cases of the problem that can be solved much more efficiently: for example, the special case Directed Steiner Tree (when we ask for paths from a root r to terminals t_1, ..., t_k) is known to be fixed-parameter tractable parameterized by the number of terminals, that is, algorithms with running time of the form f(k)*n^{O(1)} exist for the problem. On the other hand, the special case Strongly Connected Steiner Subgraph (when we ask for a path from every t_i to every other t_j) is known to be W[1]-hard parameterized by the number of terminals, hence it is unlikely to be fixed-parameter tractable. In the talk, we survey results on parameterized algorithms for special cases of Directed Steiner Network, including a recent complete classification result (joint work with Andreas Feldmann) that systematically explores the complexity landscape of directed Steiner problems to fully understand which special cases are FPT or W[1]-hard.

BibTeX - Entry

@InProceedings{marx:LIPIcs:2016:6053,
  author =	{D{\'a}niel Marx},
  title =	{{The Complexity Landscape of Fixed-Parameter Directed Steiner Network Problems (Invited Talk)}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{32:1--32:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Rasmus Pagh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6053},
  URN =		{urn:nbn:de:0030-drops-60535},
  doi =		{10.4230/LIPIcs.SWAT.2016.32},
  annote =	{Keywords: Directed Steiner Tree, Directed Steiner Network, fixed-parameter tractability, dichotomy}
}

Keywords: Directed Steiner Tree, Directed Steiner Network, fixed-parameter tractability, dichotomy
Collection: 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)
Issue Date: 2016
Date of publication: 22.06.2016

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