Simple and improved parameterized algorithms for multiterminal cuts

Theory of Computing Systems

Volumn 46, Issue 4, 2010, Pages 723-736

  Xiao, Mingyu ^a  

^a UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Graph algorithm; Multicut; Multiterminal cut; Parameterized algorithm

Indexed keywords

GRAPH ALGORITHMS; MULTICUTS; MULTITERMINAL CUT; NON-TERMINAL VERTICES; PARAMETERIZED ALGORITHM; POLYNOMIAL-TIME; TIME ALGORITHMS; UNWEIGHTED GRAPHS;

ALGORITHMS;

GRAPH THEORY;

EID: 77951205916     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-009-9215-5     Document Type: Article

References (28)

1. Xiao, M.: Algorithms for multiterminal cuts. In: Hirsch, E. A., Razborov, A. A., Semenov, A. L., Slissenko, A. (eds.) CSR. Lecture Notes in Computer Science, vol. 5010, pp. 314-325. Springer, Berlin (2008).
2. Dahlhaus, E., Johnson, D., Papadimitriou, C., Seymour, P., Yannakakis, M.: The complexity of multiterminal cuts. SIAM J. Comput. 23(4), 864-894 (1994). A preliminary version appeared in STOC 1992.
3. Yeh, W. C.: A simple algorithm for the planar multiway cut problem. J. Algorithms 39(1), 68-77 (2001).
4. Costa, M. C., Létocart, L., Roupin, F.: Minimal multicut and maximal integer multiflow: A survey. Eur. J. Oper. Res. 162(1), 55-69 (2005).
5. Cǎlinescu, G., Karloff, H. J., Rabani, Y.: An improved approximation algorithm for multiway cut. J. Comput. Syst. Sci. 60(3), 564-574 (2000). A preliminary version appeared in STOC 1998.
6. Karger, D. R., Klein, P. N., Stein, C., Thorup, M., Young, N. E.: Rounding algorithms for a geometric embedding relaxation of minimum multiway cut. In: Proceedings of the 31th Annual ACM Symposium on Theory of Computing (STOC 1999), pp. 668-678 (1999).
7. Garg, N., Vazirani, V. V., Yannakakis, M.: Multiway cuts in node weighted graphs. J. Algorithms 50(1), 49-61 (2004).
8. Naor, J., Zosin, L.: A 2-approximation algorithm for the directed multiway cut problem. SIAM J. Comput. 31(2), 477-482 (2001). A preliminary version appeared in FOCS 1997.
9. Hartvigsen, D.: The planar multiterminal cut problem. Discrete Appl. Math. 85(3), 203-222 (1998).
10. Chen, D. Z., Wu, X.: Efficient algorithms for k-terminal cuts on planar graphs. Algorithmica 38(2), 299-316 (2003).
11. Marx, D.: Parameterized graph separation problems. Theor. Comput. Sci. 351(3), 394-406 (2006). A preliminary version appeared in IWPEC 2004.
12. Chen, J., Liu, Y., Lu, S.: An improved parameterized algorithm for the minimum node multiway cut problem. In: Proceedings of the 10th International Workshop on Algorithms and Data Structures (WADS 2007), pp. 495-506. Algorithmica (2007, to appear).
13. Guillemot, S.: FPT algorithms for path-transversals and cycle-transversals problems in graphs. In: Grohe, M., Niedermeier, R. (eds.) IWPEC. Lecture Notes in Computer Science, vol. 5018, pp. 129-140. Springer, Berlin (2008).
14. Feige, U., Mahdian, M.: Finding small balanced separators. In: Proceedings of the 38th Annual ACM symposium on Theory of Computing (STOC 2006), pp. 375-384 (2006).
15. Downey, R., Fellows, M.: Parameterized Complexity. Springer, New York (1999).
16. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Berlin (2006).
17. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006).
18. Cǎlinescu, G., Fernandes, C. G., Reed, B. A.: Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width. J. Algorithms 48(2), 333-359 (2003).
19. Guo, J., Huffner, F., Kenar, E., Niedermeier, R., Uhlmann, J.: Complexity and exact algorithms for vertex multicut in interval and bounded treewidth graphs. Eur. J. Oper. Res. 186(2), 542-553 (2008). A preliminary version appeared in SOFSEM 2006.
20. Ford, J., Fulkerson, D.: Flows in Networks. Princeton University Press, Princeton (1962).
21. Goldschmidt, O., Hochbaum, D.: A polynomial algorithm for the k-cut problem for fixed k. Math. Oper. Res. 19(1), 24-37 (1994). A preliminary version appeared in FOCS 1988.
22. Xiao, M.: An improved divide-and-conquer algorithm for finding all minimum k-way cuts. In: Hong, S. H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC. Lecture Notes in Computer Science, vol. 5369, pp. 208-219. Springer, Berlin (2008).
23. Goldberg, A. V., Rao, S.: Beyond the flow decomposition barrier. J. ACM 45(5), 783-797 (1998). A preliminary version appeared in FOCS 1997.
24. Dinic, E.: Algorithm for solution of a problem of maximum flow in networks with power estimation. Sov. Math. Dokl. 11, 1277-1280 (1970).
25. n). J. Algorithms 54(2), 168-204 (2005).
26. Hu, T. C.: Multi-commodity network flows. Oper. Res. 11(3), 344-360 (1963).
27. Itai, A.: Two-commodity flow. J. ACM 25(4), 596-611 (1978).
28. Garg, N., Vazirani, V. V., Yannakakis, M.: Approximate max-flow min-(multi)cut theorems and their applications. SIAM J. Comput. 25(2), 235-251 (1996).