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

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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 ·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 ·m) time for a...

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Improved Fixed-Parameter Algorithms for Two Feedback Set Problems

Settling a ten years open question, we show that the NPcomplete Feedback Vertex Set problem is deterministically solvable in O(c ·m) time, where m denotes the number of graph edges, k denotes the size of the feedback vertex set searched for, and c is a constant. As a second result, we present a fixed-parameter algorithm for the NPcomplete Edge Bipartization problem with runtime O(2 ·m).

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ژورنال

عنوان ژورنال: Journal of Computer and System Sciences

سال: 2006

ISSN: 0022-0000

DOI: 10.1016/j.jcss.2006.02.001