On the Hardness of Approximating Max k-Cut and Its Dual
نویسندگان
چکیده
We study the Max k-Cut problem and its dual, the Abstract-1 Min k-Partition problem. In the Min k-Partition problem, given a graph G = (V, E) and positive edge weights, we want to find an edge set of minimum weight whose removal makes G k-colorable. For the Max k-Cut problem we show that, if P 6= NP, no polynomial time approximation algorithm can achieve a relative error better than 1/(34k). It is well known that a relative error of 1/k is obtained by a naive randomized heuristic. For the Min k-Partition problem, we show that for k > 2 and for Abstract-2 every > 0, there exists a constant α such that the problem cannot be approximated within α|V |2− , even for dense graphs. Both problems are directly related to the frequency allocation problem for cellular (mobile) telephones, an application of industrial relevance.
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