Algorithm for Online 3-Path Vertex Cover

A vertex set C of a graph G = ( V , E ) is a 3-path vertex cover if every path on 3 vertices has at least one vertex in C . This paper studies the online version of the minimum 3-path vertex cover problem, in which vertices are revealed one by one, and one has to determine whether the newly revealed...

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Published inTheory of computing systems Vol. 64; no. 2; pp. 327 - 338
Main Authors Zhang, Yubai, Zhang, Zhao, Shi, Yishuo, Li, Xianyue
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2020
Springer Nature B.V
Subjects
Apexes
Computer Science
Natural algorithms
Theory of Computation
Online algorithm
3-path vertex cover
Online AccessGet full text
ISSN1432-4350
1433-0490
DOI10.1007/s00224-019-09944-w

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Summary:A vertex set C of a graph G = ( V , E ) is a 3-path vertex cover if every path on 3 vertices has at least one vertex in C . This paper studies the online version of the minimum 3-path vertex cover problem, in which vertices are revealed one by one, and one has to determine whether the newly revealed vertex should be chosen into the solution without knowing future information. We show that a natural algorithm has competitive ratio at most Δ, where Δ is the maximum degree of the graph. An example is given showing that the ratio is tight.
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-019-09944-w