The planar multiterminal cut problem

Discrete Applied Mathematics

Volumn 85, Issue 3, 1998, Pages 203-222

  Hartvigsen, David ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009001530     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(98)00036-5     Document Type: Article

References (25)

1. R.E. Bixby, Matroids and operations research, in: H.S. Greenberg, F.H. Murphy, S.H. Shaw (Eds.), Advanced Techniques in the Practice of Operations Research, North-Holland, New York, 1982, pp. 333-458.
2. S. Chopra, M.R. Rao, On the multiway cut polyhedron, Networks 21 (1991) 51-89.
3. W.H. Cunningham, The optimal multiterminal cut problem, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 5, 1991, pp. 105-120.
4. E. Dahlhaus, D.S. Johnson, C.H. Papadimitriou, P. Seymour, M. Yannakakis, The complexity of multiway cuts, SIAM J. Comput. 23 (1994) 864-894.
5. M. Fiala, The minimum 3-cut problem: an application of polyhedral combinatorics, honors project, Carleton University, 1986.
6. L.R. Ford, D.R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, NJ, 1962.
7. G.N. Frederickson, Fast algorithms for shortest paths in planar graphs, with applications, SIAM. J. Comput. 16 (6) (1987) 1004-1022.
8. O. Goldschmidt, D.S. Hochbaum, A polynomial algorithm for the k-cut problem for fixed k, Math. Oper. Res. 19 (1) (1994) 24-37.
9. R.E. Gomory, T.C. Hu, Multi-terminal network flows, SIAM J. Appl. Math. 9 (1961) 551-570.
10. D. Hartvigsen, Minimum path bases, J. Algorithms 15 (1993) 125-142.
11. D. Hartvigsen, R. Mardon, The all-pairs min cut problem and the min cycle basis problem on planar graphs, SIAM J. Discrete Math. 7 (3) (1994).
12. D. Hartvigsen, F. Margot, Multiterminal flows and cuts, Oper. Res. Lett. 17 (1995) 201-204.
13. R. Hassin, Solution bases of multiterminal cut problems, Math. Oper. Res. 13 (4) (1988) 535-542.
14. X. He, An improved algorithm for the planar 3-cut problem, J. Algorithms 12 (1991) 23-37.
15. 2) algorithm for the planar 3-cut problem, SIAM J. Algebraic Discrete Meth. 6 (1985) 707-712.
16. T.C. Hu, Integer Programming and Network Flows, Addison-Wesley, Reading, MA, 1969.
17. P. Klein, S. Rao, M. Rauch, S. Subramanian, Faster shortest-path algorithms for planar graphs, Proc. of 26th Annual ACM Symp. on Theory of Computing, 1994, pp. 27-37.
18. J.B. Kruskal, On the shortest spanning subtree of a graph and the traveling salesman problem, Proc. Amer. Math. Soc. 7 (1956) 48-50.
19. L. Lovasz, M.D. Plummer, Matching Theory, North-Holland, Amsterdam, 1986.
20. S. MacLane, A structural characterization of planar combinatorial graphs. Duke Math. J. 3 (1937) 340-372.
21. J.C. Picard, M. Queyranne, Selected applications of minimum cuts in networks, INFOR 20 (1982) 394-422.
22. R.C. Prim, Shortest connection networks and some generalizations, Bell System Technol. J. 36 (1957) 1389-1401.
23. 2n) time, SIAM J. Comput. 12 (1) (1983) 71-81.
24. R.E. Tarjan, Data Structures and Network Algorithms, Soc. for Ind. and App. Math., Philadelphia, 1983.
25. D.J.A. Welsh, Matroid Theory, Academic Press, London, 1976.