TY - JOUR

T1 - Approximation Algorithms for Maximization Problems Arising in Graph Partitioning

AU - Feige, Uriel

AU - Langberg, Michael

PY - 2001/11

Y1 - 2001/11

N2 - Given a graph G = (V, E), a weight function w: E → R+, and a parameter k, we consider the problem of finding a subset U ⊆ V of size k that maximizes: Max-Vertex Coverk the weight of edges incident with vertices in U, Max-Dense Subgraphk the weight of edges in the subgraph induced by U, Max-Cutk the weight of edges cut by the partition (U, V \ U), Max-Uncutk the weight of edges not cut by the partition (U, V \ U). For each of the above problems we present approximation algorithms based on semidefinite programming and obtain approximation ratios better than those previously published. In particular we show that if a graph has a vertex cover of size k, then one can select in polynomial time a set of k vertices that covers over 80% of the edges.

AB - Given a graph G = (V, E), a weight function w: E → R+, and a parameter k, we consider the problem of finding a subset U ⊆ V of size k that maximizes: Max-Vertex Coverk the weight of edges incident with vertices in U, Max-Dense Subgraphk the weight of edges in the subgraph induced by U, Max-Cutk the weight of edges cut by the partition (U, V \ U), Max-Uncutk the weight of edges not cut by the partition (U, V \ U). For each of the above problems we present approximation algorithms based on semidefinite programming and obtain approximation ratios better than those previously published. In particular we show that if a graph has a vertex cover of size k, then one can select in polynomial time a set of k vertices that covers over 80% of the edges.

UR - http://www.scopus.com/inward/record.url?scp=0000801925&partnerID=8YFLogxK

U2 - 10.1006/jagm.2001.1183

DO - 10.1006/jagm.2001.1183

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AN - SCOPUS:0000801925

SN - 0196-6774

VL - 41

SP - 174

EP - 211

JO - Journal of Algorithms

JF - Journal of Algorithms

IS - 2

ER -