A new approach for approximating node deletion problems

Authors:
Michael Okun;Amnon Barak
Affiliations:
School of Computer Science, The Hebrew University of Jerusalem, Jerusalem 91904, Israel;School of Computer Science, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
Venue:
Information Processing Letters
Year:
2003

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Abstract

We present a new approach for approximating node deletion problems by combining the local ratio and the greedy multicovering algorithms. For a function f:V(G) → N, our approach allows to design a 2 + maxv∈V(G)logf(v) approximation algorithm for the problem of deleting a minimum number of nodes so that the degree of each node v in the remaining graph is at most f(v). This approximation ratio is shown to be asymptotically optimal. The new method is also used to design a 1 + (log 2)(k - 1) approximation algorithm for the problem of deleting a minimum number of nodes so that the remaining graph contains no k-bicliques.