A polynomial time algorithm to compute the connected treewidth of a series–parallel graph

It is well known that the treewidth of a graph G corresponds to the node search number where a team of searchers is pursuing a fugitive that is lazy and invisible (or alternatively is agile and visible) and has the ability to move with infinite speed via unguarded paths. Recently, monotone and conne...

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Vydáno v:Discrete Applied Mathematics Ročník 312; s. 72 - 85
Hlavní autoři: Mescoff, Guillaume, Paul, Christophe, Thilikos, Dimitrios M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 15.05.2022
Elsevier BV
Elsevier
Témata:
Algorithms
Apexes
Combinatorial algorithms
Computer Science
Connected treewidth
Discrete Mathematics
Dynamic programming
Graph classes
Graph decompositions
Graph theory
Graphs
Polynomials
Run time (computers)
Search methods
series–parallel graphs
Treewidth
Width parameters
Combinatorial algorithms
series–parallel graphs
Graph decompositions
Connected treewidth
Graph classes
Dynamic programming
Width parameters
Treewidth
ISSN:0166-218X, 1872-6771
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Shrnutí:It is well known that the treewidth of a graph G corresponds to the node search number where a team of searchers is pursuing a fugitive that is lazy and invisible (or alternatively is agile and visible) and has the ability to move with infinite speed via unguarded paths. Recently, monotone and connected node search strategies have been considered. A search strategy is monotone if it prevents the fugitive from pervading again areas from where he had been expelled and is connected if, at each step, the set of vertices that is or has been occupied by the searchers induces a connected subgraph of G. It has been shown that the corresponding connected and monotone search number of a graph G can be expressed as the connected treewidth, denoted by ctw(G), that is defined as the minimum width of a rooted tree-decomposition (X,T,r), where the union of the bags corresponding to the nodes of a path of T containing the root r is connected in G. In this paper, we initiate the algorithmic study of connected treewidth. We design a O(n2⋅logn)-time dynamic programming algorithm to compute the connected treewidth of biconnected series–parallel graphs. At the price of an extra n factor in the running time, our algorithm generalizes to graphs of treewidth at most two.
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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2021.02.039