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 \(\mathcal {O}(5^{k}kn^{2}+(5^{k}+3^{k}z)n^{2}\log n)\).
This work is supported by the National Grand Fundamental Research 973 Program of China (No.2008CB317107), the National Natural Science Foundation of China (No.60773111).
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Wang, J., Jiang, G. (2009). A Fixed-Parameter Enumeration Algorithm for the Weighted FVS Problem. In: Chen, J., Cooper, S.B. (eds) Theory and Applications of Models of Computation. TAMC 2009. Lecture Notes in Computer Science, vol 5532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02017-9_41
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DOI: https://doi.org/10.1007/978-3-642-02017-9_41
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