Connected treewidth and connected graph searching

  • Authors:

  • Pierre Fraigniaud;Nicolas Nisse

  • Affiliations:

  • CNRS, Lab. de Recherche en Informatique, Université Paris-Sud, Orsay, France;Lab. de Recherche en Informatique, Université Paris-Sud, Orsay, France

  • Venue:
  • LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
  • Year:
  • 2006

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Abstract

We give a constructive proof of the equality between treewidth and connected treewidth. More precisely, we describe an O(nk3)-time algorithm that, given any n-node width-k tree-decomposition of a connected graph G, returns a connected tree-decomposition of G of width ≤ k. The equality between treewidth and connected treewidth finds applications in graph searching problems. First, using equality between treewidth and connected treewidth, we prove that the connected search number cs(G) of a connected graph G is at most logn+1 times larger than its search number. Second, using our constructive proof of equality between treewidth and connected treewidth, we design an $O(log n\sqrt{log OPT}$)-approximation algorithm for connected search, running in time O(t(n)+nk3log3/2k+mlog n) for n-node m-edge connected graphs of treewidth at most k, where t(n) is the time-complexity of the fastest algorithm for approximating the treewidth, up to a factor $O(\sqrt{log OPT}$).