Constructing cactus representation for all minimum cuts in an undirected network

Journal of the Operations Research Society of Japan

Volumn 39, Issue 2, 1996, Pages 135-158

  Nagamochi, Hiroshi ^a   Kameda, Tiko ^b  

^a KYOTO UNIVERSITY   (Japan)

^b SIMON FRASER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038582057     PISSN: 04534514     EISSN: None     Source Type: Journal    
DOI: 10.15807/jorsj.39.135     Document Type: Article

References (20)

1. M.O. Ball and J.S. Provan: "Calculating bounds on reachability in computer networks," Networks 13 (1983) pp.253-278.
2. R.E. Bixby: "The minimum number of edges and vertices in a graph with edge connectivity n and m n-bonds," Networks 5 (1975) pp.253-298.
3. 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), A.A. Fridman (Ed.), Nauka, Moscow, (1976) pp.290-306.
4. S. Even and R.E. Tarjan: "Network flow and testing graph connectivity," SIAM J. Computing 4 (1975) pp.507-518.
5. L.R. Ford and D.R. Fulkerson: Flows in Networks, Princeton University Press, Princeton, N.J., 1962.
6. A. Frank, T. Ibaraki and H. Nagamochi: "On sparse subgraphs preserving connectivity properties," J. Graph Theory 17 (1993) 275-281.
7. H.N. Gabow: "A matroid approach to finding edge connectivity and packing, arborescences," Proc. 23rd ACM Symp. Theory of Computing, (1991) pp.112-122.
8. H.N. Gabow: "Applications of a poset representation to edge connectivity and graph rigidity," Proc. 32nd IEEE Symp. Found. Comp. Sci., (1991) pp.812-821.
9. R.E. Gomory and T.C. Hu: "Multi-terminal network network flows,"' J. SIAM 9 (1961) pp.551-570.
10. J. Hao and J.B. Orlin: "A faster algorithm for finding the minimum cut in a graph," Proc. 3rd ACM-SIAM Symp. on Discrete Algorithms (1992) pp.165-174.
11. A.V. Karzanov and E.A. Timofeev: "Efficient algorithm for finding all minimal edge cuts of a nonoriented graph," Kibernetika 2 (1986) pp.8-12;
12. translated in Cybernetics (1986) pp.156-162.
13. D.W. Matula: "Determining edge connectivity in O(nm)," Proc. 28th IEEE Symp. Found. Comp. Sci. (1987) pp.249-251.
14. H. Nagamochi and T. Ibaraki: "A linear-time algorithm for finding a sparse k-connected spanning subgraph of a k-connected graph," Algorithmica 7 (1992) pp.583-596.
15. H. Nagamochi and T. Ibaraki: "Computing edge-connectivity in multigraphs and capacitated graphs," SIAM J. Discrete Mathematics 5 (1992) pp.54-66.
16. H. Nagamochi, Z. Sun and T. Ibaraki: "Counting the number of minimum cuts in undirected multigraphs," IEEE Trans, on Reliability 40 (1991) pp.610-614.
17. H. Nagamochi and T. Kameda: "Canonical cactus representation for minimum cuts," Japan J. of Industrial and Applied Mathematics 11 (1994) pp.343-361.
18. D. Naor, D. Gusfield and C. Martel: "A fast algorithm for optimally increasing the edge connectivity," Proc. 31st Annual IEEE Symp. Found. Comp. Sci. (1990) pp.698-707.
19. D. Naor and V.V. Vazirani: "Representing and enumerating edge connectivity cuts in RNC," Proc. 2nd Workshop on Algorithms and Data Structures (F.Dehne, J.-R. Sack and N. Santoro, eds.), Lecture Notes in Computer Science 519, Springer Verlag, (1991) pp.273-285.
20. J.C. Picard and M. Queyranne: "On the structure of all minimum cuts in a network and applications," Mathematical Programming Study 13 (1980) pp.8-16.