A fast algorithm for computing minimum 3-way and 4-way cuts

Mathematical Programming, Series B

Volumn 88, Issue 3, 2000, Pages 507-520

  Nagamochi, Hiroshi ^a   Ibaraki, Toshihide ^b  

^a TOYOHASHI UNIVERSITY OF TECHNOLOGY   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

Graphs; Hypergraphs; k way cuts; Minimum cuts; Polynomial algorithm; Submodular function

Indexed keywords

EID: 4243094422     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00011383     Document Type: Article

References (30)

1. Burlet, M., Goldschmidt, O. (1997): A new and improved algorithm for the 3-cut problem. Oper. Res. Lett. 21, 225-227
2. Even, S., Tarjan, R.E. ( 1975): Network flow and testing graph connectivity. SIAM J. Comput. 4, 507-518
3. Goldberg, A.V., Tarjan, R.E. (1988): A new approach to the maximum flow problem. J. ACM 35, 921-940
4. Grötschel, M., Lovász, L., Schrijver, A. (1988): Geometric Algorithms and Combinatorial Optimization. Springer, Berlin
5. Goldschmidt, O., Hochbaum, D.S. (1994): A polynomial algorithm for the k-cut problem for fixed k. Math. Oper. Res. 19, 24-37
6. Hamacher, H.W., Picard, J.-C., Queyranne, M. (1984): Ranking the cuts and cut-sets of a network. Ann. Discrete Appl. Math. 19, 183-200
7. Harnacher, H.W., Picard, J.-C., Queyranne, M. (1984): On finding the K best cuts in a network. Oper. Res. Lett. 2, 303-305
8. Hao, J., Orlin, J. (1994): A faster algorithm for finding the minimum cut in a directed graph. J. Algorithms 17, 424-446
9. Henzinger, M.R., Klein, P., Rao, S., Williamson, D. (1997): Faster shortest-path algorithms for planar graphs. J. Comp. Syst. Sc. 53, 2-23
10. 2) algorithm for the planar 3-cut problem. SIAM J. Algebraic Discrete Methods 6, 707-712
11. Jünger, M., Reinelt, G., Rinaldi, G. (1995): The traveling salesman problem. In: Ball, M., Magnanti, T., Monma, C.L., Nemhauser, G.L., eds., Handbook on Operations Research and Management Sciences, 7. North-Holland, Amsterdam, pp. 225-330
12. Kamidoi, Y., Wakabayashi, S., Yoshida, N. (1997): Faster algorithms for finding a minimum k-way cut in a weighted graph. Proceedings IEEE International Symposium on Circuits and Systems, pp. 1009-1012
13. Kapoor, S. (1996): On minimum 3-cuts and approximating k-cuts using cut trees. Lect. Notes Comput. Sci. 1084, Springer, pp. 132-146
14. Karger, D.R. (1996): Minimum cuts in near-linear time. Proceedings 28th ACM Symposium on Theory of Computing, pp. 56-63
15. 2) algorithm for minimum cuts. Proceedings 25th ACM Symposium on Theory of Computing, pp. 757-765
16. Karger, D.R., Stein, C. (1996): A new approach to the minimum cut problems. J. ACM 43, 601-640
17. Karzanov, A.V. (1973): O nakhozhdenii maksimal'nogo potoka v setyakh spetsial'nogo vida i nekotorykh prilozheniyakh. In: Mathematicheskie Voprosy Upravleniya Proizvodstvom 5. Moscow State University Press, Moscow.
18. In Russian; title translation: On finding maximum flows in networks with special structure and some applications
19. Katoh, N., Ibaraki, T., Mine, H. (1982): An efficient algorithm for K shortest simple paths. Networks 12, 441-427
20. Klimmek, R., Wagner, F. (1996): A simple hypergraph min cut algorithm. Technical Report B 96-02, Department of Mathematics and Computer Science, Freie Universität Berlin
21. Lawler, E.L. (1973): Cutsets and partitions of hypergraphs. Networks 3, 275-285
22. Lee, C.H., Kim, M., Park, C.I. (1990): An efficient k-way graph partitioning algorithm for task allocation in parallel computing systems. Proceedings IEEE International Conference on Computer-Aided Design, pp. 748-751
23. Lengaur, T. (1990): Combinatorial Algorithms for Integrated Circuit Layout. Wiley
24. Nagamochi, H., Ibaraki, T. (1992): Computing the edge-connectivity of multigraphs and capacitated graphs. SIAM J. Discrete Math. 5, 54-66
25. Naaamochi, H., Ibaraki, T. (1998): A note on minimizing submodular functions. Inf. Process. Lett. 67, 239-244
26. Nagamochi, H., Nishimura, K., Ibaraki, T. (1997): Computing all small cuts in undirected networks. SIAM J. Discrete Math. 10, 469-481
27. Nagamochi, H., Katayama, S., Ibaraki, T. (1999): A faster algorithm for computing minimum 5-way and 6-way cuts in graphs. Lect. Notes Comput. Sci. 1627, Springer, pp. 164-173
28. Queyranne, M. (1998): Minimizing symmetric submodular functions. Math. Program. 82, 3-12
29. Stoer, M. (1992): Design of surviable networks. Lecture Notes Math. 1531, Springer, Heidelberg
30. Vazirani, V.V., Yannakakis, M. (1992): Suboptimal cuts: their enumeration, weight, and number. Lect. Notes Comput. Sci. 623, Springer, pp. 366-377