Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization

We show that the NP-complete Feedback Vertex Set problem, which asks for the smallest set of vertices to remove from a graph to destroy all cycles, is deterministically solvable in O ( c k ⋅ m ) time. Here, m denotes the number of graph edges, k denotes the size of the feedback vertex set searched f...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 72; no. 8; pp. 1386 - 1396
Main Authors: Guo, Jiong, Gramm, Jens, Hüffner, Falk, Niedermeier, Rolf, Wernicke, Sebastian
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2006
Subjects:
Feedback set problem
Fixed-parameter tractability
Graph algorithm
Graph modification problem
Iterative compression
Iterative compression
Feedback set problem
Fixed-parameter tractability
Graph modification problem
Graph algorithm
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary:We show that the NP-complete Feedback Vertex Set problem, which asks for the smallest set of vertices to remove from a graph to destroy all cycles, is deterministically solvable in O ( c k ⋅ m ) time. Here, m denotes the number of graph edges, k denotes the size of the feedback vertex set searched for, and c is a constant. We extend this to an algorithm enumerating all solutions in O ( d k ⋅ m ) time for a (larger) constant d. As a further result, we present a fixed-parameter algorithm with runtime O ( 2 k ⋅ m 2 ) for the NP-complete Edge Bipartization problem, which asks for at most k edges to remove from a graph to make it bipartite.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2006.02.001