TY - GEN

T1 - A unified framework for obtaining improved approximation algorithms for maximum graph bisection problems

AU - Halperin, Eran

AU - Zwick, Uri

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001.

PY - 2001

Y1 - 2001

N2 - We obtain improved semidefinite programming based approximation algorithms for all the natural maximum bisection problems of graphs. Among the problems considered are: MAX n/2-BISECTION -partition the vertices of a graph into two sets of equal size such that the total weight of edges connecting vertices from different sides is maximized; MAX n/2-VERTEX-COVER - find a set containing half of the vertices such that the total weight of edges touching this set is maximized; MAX n/2-DENSE-SUBGRAPH - find a set containing half of the vertices such that the total weight of edges connecting two vertices from this set is maximized; and MAX n/2-UnCUT - partition the vertices into two sets of equal size such that the total weight of edges that do not cross the cut is maximized. We also consider the directed versions of these problems, MAX n/2-DIRECTED-BISECTION and MAX n/2-DIRECTED-UnCUT. These results can be used to obtain improved approximation algorithms for the unbalanced versions of the partition problems mentioned above, where we want to partition the graph into two sets of size k and n — k, where k is not necessarily f. Our results improve, extend and unify results of Frieze and Jerrum, Feige and Langberg, Ye, and others.

AB - We obtain improved semidefinite programming based approximation algorithms for all the natural maximum bisection problems of graphs. Among the problems considered are: MAX n/2-BISECTION -partition the vertices of a graph into two sets of equal size such that the total weight of edges connecting vertices from different sides is maximized; MAX n/2-VERTEX-COVER - find a set containing half of the vertices such that the total weight of edges touching this set is maximized; MAX n/2-DENSE-SUBGRAPH - find a set containing half of the vertices such that the total weight of edges connecting two vertices from this set is maximized; and MAX n/2-UnCUT - partition the vertices into two sets of equal size such that the total weight of edges that do not cross the cut is maximized. We also consider the directed versions of these problems, MAX n/2-DIRECTED-BISECTION and MAX n/2-DIRECTED-UnCUT. These results can be used to obtain improved approximation algorithms for the unbalanced versions of the partition problems mentioned above, where we want to partition the graph into two sets of size k and n — k, where k is not necessarily f. Our results improve, extend and unify results of Frieze and Jerrum, Feige and Langberg, Ye, and others.

UR - http://www.scopus.com/inward/record.url?scp=84947262091&partnerID=8YFLogxK

U2 - 10.1007/3-540-45535-3_17

DO - 10.1007/3-540-45535-3_17

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AN - SCOPUS:84947262091

SN - 3540422250

SN - 9783540422259

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 210

EP - 225

BT - Integer Programming and Combinatorial Optimization - 8th International IPCO Conference, Proceedings

A2 - Aardal, Karen

A2 - Gerards, Bert

PB - Springer Verlag

T2 - 8th International Integer Programming and Combinatorial Optimization Conference, IPCO 2001

Y2 - 13 June 2001 through 15 June 2001

ER -