Approximating dense cases of covering problems
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چکیده
We study dense instances of several covering problems An in stance of the set cover problem with m sets is dense if there is such that any element of the ground set X belongs to at least m sets We show that the dense set cover problem can be approximated with the performance ratio c log jX j for any c though it is unlikely to be NP hard A polynomial time approximation scheme is constructed for the dense Steiner tree problem in n vertex graphs i e for the case when each terminal is adjacent to at least n vertices We also study the vertex cover problem in dense graphs i e graphs with the bounded minimum or average vertex degree A better approximation algorithm is suggested Its performance ratio is and p for graphs with jV j bounded minimum and average vertex degree respectively We also consider superdense complementary to sparse cases of all these problems
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تاریخ انتشار 1997