A Linear Time Algorithm for a Variant of the MAX CUT Problem in Series Parallel Graphs

Given a graph G=V,E, a connected sides cut U,V\U or δU is the set of edges of E linking all vertices of U to all vertices of V\U such that the induced subgraphs GU and GV\U are connected. Given a positive weight function w defined on E, the maximum connected sides cut problem (MAX CS CUT) is to find...

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Bibliographic Details
Published inAdvances in Operations Research Vol. 2017; no. 2017; pp. 1 - 4
Main Author Chaourar, Brahim
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2017
Hindawi
John Wiley & Sons, Inc
Subjects
Algorithms
Graphs
Labeling
Operations research
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ISSN1687-9147
1687-9155
1687-9155
DOI10.1155/2017/1267108

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Summary:Given a graph G=V,E, a connected sides cut U,V\U or δU is the set of edges of E linking all vertices of U to all vertices of V\U such that the induced subgraphs GU and GV\U are connected. Given a positive weight function w defined on E, the maximum connected sides cut problem (MAX CS CUT) is to find a connected sides cut Ω such that wΩ is maximum. MAX CS CUT is NP-hard. In this paper, we give a linear time algorithm to solve MAX CS CUT for series parallel graphs. We deduce a linear time algorithm for the minimum cut problem in the same class of graphs without computing the maximum flow.
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ISSN:1687-9147
1687-9155
1687-9155
DOI:10.1155/2017/1267108