Fixed-Parameter Tractability for Subset Feedback Set Problems with Parity Constraints
Fixed-Parameter Tractability for Subset Feedback Set Problems with Parity Constraints
复制标题
具有奇偶约束的子集反馈集问题的固定参数可处理性
DOI：
10.1016/j.tcs.2015.02.004
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发表时间：
2015
影响因子：
1.1
通讯作者：
Naonori Kakimura and Ken-ichi Kawarabayashi
中科院分区：
文献类型：
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作者：
Hanna Sumita;Naonori Kakimura;and Kazuhisa Makino;Naonori Kakimura and Ken-ichi Kawarabayashi
子集反馈集问题是著名的反馈顶点集问题的推广，它是指给定一个无向图G，G的顶点子集S和正整数k，目标是找到一个顶点集X，其大小不超过k，使得G-X没有S-圈，其中S-圈是至少有一个顶点S的圈。最近的研究表明，这个问题是固定参数易处理的，其中k是参数。在本文中，我们进一步推广这个问题的奇偶约束，并证明了固定参数的易处理性：1。对于一个参数k，存在一个固定参数算法，它要么找到一个大小为k的顶点集X，使得G-X没有偶数长度的S-圈，要么得出这样的顶点集不存在的结论。2.对于一个参数k，存在一个固定参数算法，它要么找到一个大小为k的顶点集X，使得G-X没有奇数长度的S-圈，要么得出这样的顶点集不存在的结论。
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.