Institut für Informatik   Abteilung V

 Universität Bonn -> Institut für Informatik -> Abteilung V CS-Reports 1996 Copyright 1996 Universität Bonn, Institut für Informatik, Abt. V 85160 Approximating Dense Cases of Covering Problems Marek Karpinski, Alexander Zelikovsky [Download PostScript] [Download PDF] We study dense cases of several covering problems. An instance of the set cover problem with $m$ sets is dense if there is $\epsilon>0$ such that any element belongs to at least $\epsilon m$ sets. We show that the dense set cover problem can be approximated with the performance ratio $c\log n$ for any $c>0$ and it is unlikely to be NP-hard. We construct a polynomial-time approximation scheme for the dense Steiner tree problem in $n$-vertex graphs, i.e. for the case when each terminal is adjacent to at least $\epsilon n$ vertices. We also study the vertex cover problem in $\epsilon$-dense graphs. Though this problem is shown to be still MAX-SNP-hard as in general graphs, we find a better approximation algorithm with the performance ratio $2\over{1+\epsilon}$. The {\em superdense} cases of all these problems are shown to be solvable in polynomial time. Last Change: 11/05/14 at 10:01:20  English Universität Bonn -> Institut für Informatik -> Abteilung V