Abstract
A subset FcV of vertices of a digraph G=(V,A) with n vertices and m arcs, is called a feedback vertex set (fvs), if G-F is an acyclic digraph (dag). The main results in this paper are:
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(1)
An O(n2m) simplification procedure is developed and it is shown that the class of digraphs, for which a minimum fvs is determined by this procedure alone, properly contains two classes for which minimum fvs's are known to be computable in polynomial time, see [13,15].
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(2)
A new O(n3·|F|) approximation algorithm MFVS for the fvs-problem is proposed, which iteratively deletes in each step a vertex with smallest mean return time during a random walk in the digraph. It is shown that MFVS applied to symmetric digraphs determines a solution of worst case ratio bounded by O(log n). The quality of fvs's produced by MFVS is compared to those produced by Rosen's fvs-algorithm, see [11], for series of randomly generated digraphs.
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© 1990 Springer-Verlag Berlin Heidelberg
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Speckenmeyer, E. (1990). On feedback problems in digraphs. In: Nagl, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 1989. Lecture Notes in Computer Science, vol 411. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52292-1_16
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DOI: https://doi.org/10.1007/3-540-52292-1_16
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