We give a O(max{12k, (41gk)k} · n ω) algorithm for testing whether an undirected graph on n vertices has a feedback vertex set of size at most k where O(n ω) is the complexity of the best matrix multiplication algorithm. The previous best fixed parameter tractable algorithm for the problem took O((2k + 1) k n) time. The main technical lemma we prove and use to develop our algorithm is that that there exists a constant c such that, if an undirected graph on n vertices with minimum degree 3 has a feedback vertex set of size at most c√n, then the graph will have a cycle of length at most 12. This lemma may be of independent interest. We also show that the feedback vertex set problem can be solved in O(dkkn) for some constant d in regular graphs, almost regular graphs and (fixed) bounded degree graphs. © Springer-Verlag Berlin Heidelberg 2002.
CITATION STYLE
Raman, V., Saurabh, S., & Subramanian, C. R. (2002). Faster fixed parameter tractable algorithms for undirected feedback vertex set. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2518 LNCS, pp. 241–248). https://doi.org/10.1007/3-540-36136-7_22
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