Abstract
The input of the Edge Multicut problem consists of an undirected graph G and pairs of terminals {s 1,t 1}, ..., {s m ,t m }; the task is to remove a minimum set of edges such that s i and t i are disconnected for every 1 ≤ i ≤ m. The parameterized complexity of the problem, parameterized by the maximum number k of edges that are allowed to be removed, is currently open. The main result of the paper is a parameterized 2-approximation algorithm: in time f(k)·n O(1), we can either find a solution of size 2k or correctly conclude that there is no solution of size k.
The proposed algorithm is based on a transformation of the Edge Multicut problem into a variant of parameterized Max-2-SAT problem, where the parameter is related to the number of clauses that are not satisfied. It follows from previous results that the latter problem can be 2-approximated in a fixed-parameter time; on the other hand, we show here that it is W[1]-hard. Thus the additional contribution of the present paper is introducing the first natural W[1]-hard problem that is constant-ratio fixed-parameter approximable.
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Marx, D., Razgon, I. (2009). Constant Ratio Fixed-Parameter Approximation of the Edge Multicut Problem. In: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_58
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DOI: https://doi.org/10.1007/978-3-642-04128-0_58
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