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.ICALP.2016.149
URN: urn:nbn:de:0030-drops-62936
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6293/
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Axiotis, Kyriakos ; Fotakis, Dimitris

On the Size and the Approximability of Minimum Temporally Connected Subgraphs

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Abstract

We consider temporal graphs with discrete time labels and investigate the size and the approximability of minimum temporally connected spanning subgraphs. We present a family of minimally connected temporal graphs with n vertices and Omega(n^2) edges, thus resolving an open question of (Kempe, Kleinberg, Kumar, JCSS 64, 2002) about the existence of sparse temporal connectivity certificates. Next, we consider the problem of computing a minimum weight subset of temporal edges that preserve connectivity of a given temporal graph either from a given vertex r (r-MTC problem) or among all vertex pairs (MTC problem). We show that the approximability of r-MTC is closely related to the approximability of Directed Steiner Tree and that r-MTC can be solved in polynomial time if the underlying graph has bounded treewidth. We also show that the best approximation ratio for MTC is at least O(2^{log^{1-epsilon}(n)} and at most O(min{n^{1+epsilon},(Delta*M)^{2/3+epsilon}), for any constant epsilon > 0, where M is the number of temporal edges and Delta is the maximum degree of the underlying graph. Furthermore, we prove that the unweighted version of MTC is APX-hard and that MTC is efficiently solvable in trees and 2-approximable in cycles.

BibTeX - Entry

@InProceedings{axiotis_et_al:LIPIcs:2016:6293,
  author =	{Kyriakos Axiotis and Dimitris Fotakis},
  title =	{{On the Size and the Approximability of Minimum Temporally Connected Subgraphs}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{149:1--149:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6293},
  URN =		{urn:nbn:de:0030-drops-62936},
  doi =		{10.4230/LIPIcs.ICALP.2016.149},
  annote =	{Keywords: Temporal Graphs, Temporal Connectivity, Approximation Algorithms}
}

Keywords: Temporal Graphs, Temporal Connectivity, Approximation Algorithms
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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