We present a new parameterized algorithm for the feedback vertex set problem (fvs) on undirected graphs. We approach the problem by considering a variation of it, the disjoint feedback vertex set problem (disjoint-fvs), which finds a feedback vertex set of size k that has no overlap with a given feedback vertex set F of the graph G. We develop an improved kernelization algorithm for disjointfvs and show that disjoint-fvs can be solved in polynomial time when all vertices in G \ F have degrees upper bounded by three. We then propose a new branch-and-search process on disjointfvs, and introduce a new branch-and-search measure. The process effectively reduces a given graph to a graph on which disjoint-fvs becomes polynomial-time solvable, and the new measure more accurately evaluates the efficiency of the process. These algorithmic and combinatorial studies enable us to develop an O * (3.83 k )-time parameterized algorithm for the general fvs problem, improving all previous algorithms for the problem.

No abstract

No abstract

No abstract

No abstract