Canonical cactus representation for minimum cuts
- 65 Downloads
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.
Key wordsundirected multigraph cactus representation minimum cut canonical form isomorphism
Unable to display preview. Download preview PDF.
- E.A. Dinits, A.V. Karzanov and M.V. Lomonosov, On the structure of a family of minimal weighted cuts in a graph. Studies in Discrete Optimization (in Russian), (ed. A.A. Fridman), Nauka, Moscow, 1976, 290–306.Google Scholar
- H.N. Gabow, Applications of a poset representation to edge connectivity and graph rigidity. Proc. 32nd IEEE Symp. Found. Comp. Sci., 1991, 812–821.Google Scholar
- H. Nagamochi and T. Kameda, An efficient construction of cactus representation for minimum cuts in undirected networks. Tech. Rep. CSS/LCCR TR92-04, School of Computing Science, Simon Fraser Univ., 1992.Google Scholar
- D. Naor, D. Gusfield and C. Martel, A fast algorithm for optimally increasing the edge connectivity. Proc. 31st Annual IEEE Symp. Found. Comp. Sci., St. Louis, 1990, 698–707.Google Scholar
- D. Naor and V.V. Vazirani, Representing and enumerating edge connectivity cuts inRNC. Proc. 2nd Workshop on Algorithms and Data Structures (eds. F. Dehne, J.-R. Sack and N. Santoro), Lecture Notes in Computer Science 519, Springer Verlag, Berlin-Heidelberg-New York, 1991, 273–285.CrossRefGoogle Scholar