A Linear Time Algorithm for a Variant of the MAX CUT Problem in Series Parallel Graphs
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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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A Linear Time Algorithm for the Minimum-weight Feedback Vertex Set Problem in Series-parallel Graphs
2004 ◽
Vol 20
(4)
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pp. 579-588
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2020 ◽
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1994 ◽
Vol 73
(1)
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pp. 192-198
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