1. FROM PATHWIDTH TO CONNECTED PATHWIDTH.
- Author
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DERENIOWSKI, DARIUSZ
- Subjects
- *
GRAPH theory , *MATHEMATICAL decomposition , *MATHEMATICAL inequalities , *ALGORITHMS , *MONOTONIC functions - Abstract
It is proven that the connected pathwidth of any graph G is at most 2 · pw(G)+1, where pw(G) is the pathwidth of G. The method is constructive, i.e., it yields an efficient algorithm that for a given path decomposition of width k computes a connected path decomposition of width at most 2k+1. The running time of the algorithm is O(dk²), where d is the number of "bags" in the input path decomposition. The motivation for studying connected path decompositions comes from the connection between the pathwidth and the search number of a graph. One of the advantages of the above bound for connected pathwidth is an inequality cs(G) ≤ 2s(G) + 3, where cs(G) and s(G) are the connected search number and the search number of G, respectively. Moreover, the algorithm presented in this work can be used to convert a given search strategy using k searchers into a (monotone) connected one using 2k + 3 searchers and starting at an arbitrary homebase. [ABSTRACT FROM AUTHOR]
- Published
- 2012
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