Divide-and-conquer algorithms for partitioning hypergraphs and submodular systems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5878 LNCS, Issue , 2009, Pages 55-64

  Okumoto, Kazumasa ^a   Fukunaga, Takuro ^b   Nagamochi, Hiroshi ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION FACTOR; DIVIDE-AND-CONQUER ALGORITHM; EXACT ALGORITHMS; FINITE SET; FIXED INTEGERS; HYPERGRAPH; K-PARTITION; SUBMODULAR; SUBMODULAR FUNCTIONS;

COMPUTATION THEORY; SET THEORY;

APPROXIMATION ALGORITHMS;

EID: 75649090803     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-10631-6_8     Document Type: Conference Paper

References (18)

1. Frank, A.: Applications of Submodular Functions. Surveys in Combinatorics. Cambridge London Mathematical Society Lecture Notes Series, vol. 187, pp. 85-136 (1993)
2. Fujishige, S.: Submodular Function and Optimization. North-Holland, Amsterdam (1991)
3. Fukunaga, T.: Computing Minimum Multiway Cuts in Hypergraphs from Hyper-tree Packings. Technical report, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University (2009)
4. Garg, N., Vazirani, V.V., Yannakakis, M.: Multiway Cuts in Node Weighted Graphs. J. Algorithms 50, 49-61 (2004)
5. Gasieniec, L., Jansson, J., Lingas, A., óstlin, A.: On the Complexity of Constructing Evolutionary Trees. J. Comb. Opt. 3, 183-197 (1999)
6. Goldberg, A.V., Tarjan, R.E.: A New Approach to the Maximum Flow Problem. J. ACM 35, 921-940 (1988)
7. Goldschmidt, O., Hochbaum, D.: A Polynomial Algorithm for the k-cut Problem for Fixed k. Math. Operations Research 19, 24-37 (1994)
8. Iwata, S.: Submodular Function Minimization. Math. Prog. 112, 45-64 (2008)
9. Kamidoi, Y., Yoshida, N., Nagamochi, H.: A Deterministic Algorithm for Finding All Minimum k-way Cuts. SIAM J. Comp. 36, 1329-1341 (2006)
10. Karger, D.R., Stein, C.: A New Approach to the Minimum Cut Problem. J. ACM 43, 601-640 (1996)
11. Lawler, E.L.: Cutsets and Partitions of Hypergraphs. Networks 3, 275-285 (1973)
12. Nagamochi, H.: Algorithms for the Minimum Partitioning Problems in Graphs. IEICE Trans. Inf. Sys. J86-D-1, 53-68 (2003)
13. Queyranne, M.: On Optimum Size-constrained Set Partitions. In: Proceedings of AUSSOIS (1999)
14. Thorup, M.: Minimum k-way Cuts via Deterministic Greedy Tree Packing. In: 40th Annual ACM Symposium on Theory of Computing, pp. 159-166 (2008)
15. Vazirani, V.V., Yannakakis, M.: Suboptimal Cuts: Their Enumeration, Weight and Number. In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 366-377. Springer, Heidelberg (1992)
16. Xiao, M.: Finding Minimum 3-way Cuts in Hypergraphs. In: Agrawal, M., Du, D. Z., Duan, Z., Li, A. (eds.) TAMC 2008. LNCS, vol. 4978, pp. 270-281. Springer, Heidelberg (2008)
17. 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 2008. LNCS, vol. 5369, pp. 208-219. Springer, Heidelberg (2008)
18. Zhao, L., Nagamochi, H., Ibaraki, T.: A Unified Framework for Approximating Multiway Partition Problems. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223, pp. 682-694. Springer, Heidelberg (2001)