, Volume 11, Issue 3, pp 343-361

Canonical cactus representation for minimum cuts

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Abstract

It is known that all minimum cuts in a networkN can be embedded in a cactus whose size is bounded by a linear function of the number of vertices inN, such that any minimum cut ofN can be easily obtained as a minimum cut of the cactus. However, such a representation for a given network is not unique. We introduce two canonical forms of cactus representation for the minimum cuts and show their uniqueness. These cacti contain at most twice as many vertices asN.

This work was supported in part by grants from the Natural Sciences and Engineering Research Council of Canada, the Advanced Systems Institute of British Columbia, and in part by Grant-in-Aid from the Ministry of Education, Science and Culture of Japan.