Maximum weight bipartite matching in matrix multiplication time

Theoretical Computer Science

Volumn 410, Issue 44, 2009, Pages 4480-4488

  Sankowski, Piotr ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

Matchings in graphs; Matrix multiplication; Shortest paths; Weighted perfect matchings

Indexed keywords

BIPARTITE GRAPHS; BIPARTITE MATCHINGS; EDGE WEIGHTS; MATCHINGS; MATCHINGS IN GRAPHS; MATRIX MULTIPLICATION; MATRIX MULTIPLICATION TIME; MINIMUM WEIGHT; NONNEGATIVE INTEGERS; SHORTEST PATH; SHORTEST PATHS; SINGLE SOURCE; SUBOPTIMAL SOLUTION; TIME ALGORITHMS; VERTEX COVER; VERTEX DISJOINT; WEIGHTED PERFECT MATCHINGS;

COMPUTATION THEORY; MATRIX ALGEBRA;

GRAPH THEORY;

EID: 70249146105     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2009.07.028     Document Type: Article

References (27)

1. Bellman R. On a routing problem. Quarterly of Applied Mathematics 16 1 (1958) 87-90
2. Coppersmith D., and Winograd S. Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation 9 3 (1990) 251-280
3. Cormen T.H., Leiserson C.E., and Rivest R.L. Introduction to Algorithms (1990), MIT Press, Cambridge Mass
4. Dinic E.A., and Kronrod M.A. An algorithm for the solution of the assignment problem. Soviet Mathematics Doklady 10 (1969) 1324-1326
5. Edmonds J., and Karp R.M. Theoretical improvements in algorithmic efficiency for network flow problems. Journal of ACM 19 2 (1972) 248-264
6. David Eppstein, Representing all Minimum Spanning Trees with Applications to Counting and Generation. Technical Report ICS-TR-95-50, 1995
7. Gabow H.N. Scaling algorithms for network problems. Journal of Computer and System Sciences 31 2 (1985) 148-168
8. Gabow H.N., and Tarjan R.E. Faster scaling algorithms for network problems. SIAM Journal on Computing 18 5 (1989) 1013-1036
9. Goldberg A.V. Scaling algorithms for the shortest paths problem. SIAM Journal on Computing 24 3 (1995) 494-504
10. Iri M. A new method for solving transportation-network problems. Journal of the Operations Research Society of Japan 3 (1960) 27-87
11. L.R. Ford Jr., Network Flow Theory. Paper P-923, The RAND Corperation, Santa Moncia, California, August 1956
12. Kao M.-Y., Lam T.W., Sung W.-K., and Ting H.-F. A decomposition theorem for maximum weight bipartite matchings with applications to evolutionary trees. SIAM Journal on Computing 31 1 (2001) 18-26
13. Karp R.M., Upfal E., and Wigderson A. Constructing a perfect matching is in random nc. Combinatorica 6 1 (1986) 35-48
14. Kuhn H.W. The Hungarian method for the assignment problem. Naval Research Logistics Quarterly 2 (1955) 83-97
15. Lawler E.L. Combinatorial Optimization: Networks and Matroids (1976), Holt, Rinehart and Winston, New York
16. Lovász L. On determinants, matchings and random algorithms. In: Budach L. (Ed). Fundamentals of Computation Theory (1979), Akademie-Verlag 565-574
17. Moore E.F. The shortest path through a maze. Proceedings of the International Symposium on the Theory of Switching (1959), Harvard University Press 285-292
18. Marcin Mucha, Piotr Sankowski, Maximum matchings via Gaussian elimination, in: Proceedings of the 45th annual IEEE Symposium on Foundations of Computer Science, 2004, pp. 248-255
19. Mulmuley K., Vazirani U.V., and Vazirani V.V. Matching is as easy as matrix inversion. Combinatorica 7 1 (1987) 105-113
20. Munkres J. Algorithms for the assignment and transportation problems. Journal of SIAM 5 1 (1957) 32-38
21. Rabin M.O., and Vazirani V.V. Maximum matchings in general graphs through randomization. Journal of Algorithms 10 (1989) 557-567
22. Sankowski P. Shortest paths in matrix multiplication time. Proceedings of the 13th Annual European Symposium on Algorithms. LNCS vol. 3669 (2005) 770-778
23. Schwartz J. Fast probabilistic algorithms for verification of polynomial identities. Journal of the ACM 27 (1980) 701-717
24. Shimbel A. Structure in communication nets. Proceedings of the Symposium on Information Networks (1955), Polytechnic Press of the Polytechnic Institute of Brooklyn, Brooklyn 199-203
25. Storjohann A. High-order lifting and integrality certification. Journal of Symbolic Computing 36 3-4 (2003) 613-648
26. Yuster R., and Zwick U. Answering distance queries in directed graphs using fast matrix multiplication. Proceedings of the 46th Annual Symposium on Foundations of Computer Science (2005), IEEE 90-100
27. Zippel R. Probabilistic algorithms for sparse polynomials. International Symposium on Symbolic and Algebraic Computation. Lecture Notes in Computer Science vol. 72 (1979), Springer-Verlag, Berlin 216-226