Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
نویسندگان
چکیده
منابع مشابه
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...
متن کاملSubset Feedback Vertex Set Is Fixed-Parameter Tractable
The classical FEEDBACK VERTEX SET problem asks, for a given undirected graph G and an integer k, to find a set of at most k vertices that hits all the cycles in the graph G. FEEDBACK VERTEX SET has attracted a large amount of research in the parameterized setting, and subsequent kernelization and fixed-parameter algorithms have been a rich source of ideas in the field. In this paper we consider...
متن کاملDirected Feedback Vertex Set is Fixed-Parameter Tractable
We resolve positively a long standing open question regarding the fixed-parameter tractability of the parameterized Directed Feedback Vertex Set problem. In particular, we propose an algorithm which solves this problem in O(8k! ∗ poly(n)).
متن کاملImproved 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).
متن کاملParameterized Algorithms for Feedback Vertex Set
We present an algorithm for the parameterized feedback vertex set problem that runs in time O((2 lg k + 2 lg lg k + 18)n). This improves the previous O(max{12, (4 lg k)}n) algorithm by Raman et al. by roughly a 2 factor (n ∈ O(n) is the time needed to multiply two n × n matrices). Our results are obtained by developing new combinatorial tools and employing results from extremal graph theory. We...
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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