Abstract
Polynomial-time approximation algorithms with nontrivial performance guarantees are presented for the problems of (a) partitioning the vertices of a weighted graph intok blocks so as to maximize the weight of crossing edges, and (b) partitioning the vertices of a weighted graph into two blocks of equal cardinality, again so as to maximize the weight of crossing edges. The approach, pioneered by Goemans and Williamson, is via a semidefinite programming relaxation.
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Communicated by M. X. Goemans.
The first author was supported in part by NSF Grant CCR-9225008. The work described here was undertaken while the second author was visiting Carnegie Mellon University; at that time he was a Nuffield Science Research Fellow, and was supported in part by Grant GR/F 90363 of the UK Science and Engineering Research Council, and Esprit Working Group 7097 “RAND”.
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Frieze, A., Jerrum, M. Improved approximation algorithms for MAXk-CUT and MAX BISECTION. Algorithmica 18, 67–81 (1997). https://doi.org/10.1007/BF02523688
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DOI: https://doi.org/10.1007/BF02523688