Fixed-parameter tractability for subset feedback set problems with parity constraints

The subset feedback set problem, which is a generalization of the well-known feedback vertex set problem, is that we are given an undirected graph G with a vertex subset S and a positive integer k, and the goal is to find a vertex set X of size at most k such that G−X has no S-cycle, where an S-cycl...

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Bibliographic Details
Published in:Theoretical computer science Vol. 576; pp. 61 - 76
Main Authors: Kakimura, Naonori, Kawarabayashi, Ken-ichi
Format: Journal Article
Language:English
Published: Elsevier B.V 20.04.2015
Subjects:
Algorithms
Feedback
Fixed-parameter algorithm
Graph minor theory
Graphs
Integers
Parity
Parity constraints
Subset feedback set problem
Fixed-parameter algorithm
Subset feedback set problem
Parity constraints
Graph minor theory
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:The subset feedback set problem, which is a generalization of the well-known feedback vertex set problem, is that we are given an undirected graph G with a vertex subset S and a positive integer k, and the goal is to find a vertex set X of size at most k such that G−X has no S-cycle, where an S-cycle is a cycle having at least one vertex of S. It was recently shown that this problem is fixed parameter tractable, where k is the parameter. In this paper, we further generalize this problem to one with the parity constraints, and show the fixed parameter tractability:1.For a parameter k, there exists a fixed-parameter algorithm that either finds a vertex set X of size k such that G−X has no S-cycle of even length, or concludes that such a vertex set does not exist.2.For a parameter k, there exists a fixed-parameter algorithm that either finds a vertex set X of size k such that G−X has no S-cycle of odd length, or concludes that such a vertex set does not exist.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2015.02.004