A polynomial time algorithm to compute the connected tree-width of a series-parallel graph release_umotw6wmyrhblnxmcpvqecnqoi

by Guillaume Mescoff, Christophe Paul, Dimitrios Thilikos

Released as a article .

2021  

Abstract

It is well known that the treewidth of a graph G corresponds to the node search number where a team of cops is pursuing a robber that is lazy, visible and has the ability to move at infinite speed via unguarded path. In recent papers, connected node search strategies have been considered. A search stratregy is connected if at each step the set of vertices that is or has been occupied by the team of cops, induced a connected subgraph of G. It has been shown that the connected search number of a graph G can be expressed as the connected treewidth, denoted ๐œ๐ญ๐ฐ(G), that is defined as the minimum width of a rooted tree-decomposition ( X,T,r) such that the union of the bags corresponding to the nodes of a path of T containing the root r is connected. Clearly we have that ๐ญ๐ฐ(G)โฉฝ๐œ๐ญ๐ฐ(G). It is paper, we initiate the algorithmic study of connected treewidth. We design a O(n^2ยทlog n)-time dynamic programming algorithm to compute the connected treewidth of a biconnected series-parallel graphs. At the price of an extra n factor in the running time, our algorithm genralizes to graphs of treewidth at most 2.
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Type  article
Stage   submitted
Date   2021-01-27
Version   v5
Language   en ?
arXiv  2004.00547v5
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