Abstract
While the picture of approximation complexity class becomes clear for most combinatorial optimization problems, it remains an open question whether Feedback Vertex Set can be approximated within a constant ratio in directed graph case. In this paper we present an approximation algorithm with performance bound L max −1, where L max is the largest length of essential cycles in the graph G(V,E). The worst case bound is \(\left\lfloor {\sqrt {{{\left| V \right|}^2} - \left| V \right| - \left| E \right| + 1} } \right\rfloor \) which, in general, is inferior to Seymour’s recent result [14], but becomes a small constant for some graphs. Furthermore, we prove the so-called pseudo ∈-approximate property, i.e. FVS can be divided into a class of disjoint NP -complete subproblems, and our heuristic becomes ∈-approximate for each one of these subproblems.
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© 1996 Kluwer Academic Publishers
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Qian, T., Ye, Y., Pardalos, P.M. (1996). A Pseudo ∈-Approximate Algorithm For Feedback Vertex Set. In: Floudas, C.A., Pardalos, P.M. (eds) State of the Art in Global Optimization. Nonconvex Optimization and Its Applications, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3437-8_21
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DOI: https://doi.org/10.1007/978-1-4613-3437-8_21
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