A Fixed-Parameter Enumeration Algorithm for the Weighted FVS Problem

Authors:
Jianxin Wang;Guohong Jiang
Affiliations:
School of Information Science and Engineering, Central South University, Changsha, China 410083;School of Information Science and Engineering, Central South University, Changsha, China 410083
Venue:
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Year:
2009

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Abstract

In this paper, we present a fixed-parameter enumeration algorithm for the feedback vertex set problem by using the branch-and-search method. The algorithm transforms the feedback vertex set problem to the feedback edge set problem with specific conditions. Then it enumerates the z minimum-weight feedback edge sets by enumerating the z maximum-weight forests. As a result, we show the problem of enumerating the z minimum-weight feedback vertex sets of size k is solvable in time $\mathcal {O}(5^{k}kn^{2}+(5^{k}+3^{k}z)n^{2}\log n)$.