On complexity, representation and approximation of integral multicommodity flows

Discrete Applied Mathematics

Volumn 99, Issue 1-3, 2000, Pages 183-208

  Srivastav, Anand ^a   Stangier, Peter ^b  

^a UNIVERSITY OF KIEL   (Germany)

^b UNIVERSITY OF COLOGNE   (Germany)

Author keywords

05C85; 60C05; 60E15; 68Q25; 68R10; 90C35; Derandomization; Integer programming; Integral multicommodity flows

Indexed keywords

EID: 0346043054     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(99)00133-X     Document Type: Article

References (24)

1. N. Alon, J. Spencer, P. Erdos, The Probabilistic Method, Wiley, New York, 1992.
2. Angluin D., Valiant L.G. Fast probabilistic algorithms for Hamiltonion circuits and matchings. J. Comput. Systems Sci. 18:1979;155-193.
3. Even S., Itai A., Shamir A. On the complexity of timetable and multicommodity flow problems. SIAM J. Comput. 5(4):1976;691-703.
4. M.R. Garey, D.S. Johnson, Computers and Intractability, W.H. Freeman, New York, 1979.
5. N. Garg, J. Könemann, Faster and simpler algorithms for multicommodity flow and other fractional packing problems, Technical Report, Max-Planck-Institut für Informatik, Saarbrücken, Germany, 1997.
6. Garg N., Vazirani V.V., Yannakakis M. Primal-Dual algorithms for integral flow and multicut in trees, with applications to matching and set cover. Algorithmica. 18:1997;3-20.
7. M. Grötschel, L. Lovász, A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Springer, Berlin, 1988.
8. J. Kleinberg, E. Trados, Routing with low congestion in densely embedded graphs, Preprint, 1996.
9. E. Korach, M. Penn, Tight integral duality gap in the chinese postman problem, Technical Report, Computer Science Department, Israel Institute of Technology, Haifa, 1989.
10. Korach E., Penn M. A fast algorithm for maximum integral two-commodity flow in planar graphs. Discrete Appl. Math. 47:1993;77-83.
11. T. Leighton, F. Makedon, S. Plotkin, C. Stein, E. Tardos, S. Tragondas, Fast approximation algorithms for multicommodity flow problems, Proceedings of the 23rd Annual ACM Symposium on the Theory of Computing, Baltimore, MD, 1991, pp. 101-111.
12. 2) -algorithm for finding maximum flows in networks Inform. Process. Lett. 7:1978;277-278.
13. C. McDiarmid, On the method of bounded differences, in: J. Siemons (Ed.), Surveys in Combinatorics, London Math. Soc. Lectures Notes, Series 141, Cambridge University Press, Cambridge, England, 1989.
14. R. Motwani, J. Naor, P. Raghavan, Randomized approximation algorithms in combinatorial optimization, in: D.S. Hochbaum (Ed.), Approximation Algorithms, PWS Publishers, 1995, pp. 447-481.
15. Okamura H., Seymour P.D. Multicommodity flows in planar graphs. J. Combin. Theory Ser. B. 31:1981;75-81.
16. F. Pfeiffer, Zur Komplexität des Disjunkte-Wege-Problems, Dissertation, Forschungsinstitut für Diskrete Mathematik, Universität Bonn, 1991.
17. F. Pfeiffer, Personal communication, 1992.
18. Raghavan P. Probabilistic construction of deterministic algorithms: approximating packing integer programs. J. Comput. Systems. Sci. 37:1988;130-143.
19. Raghavan P., Thompson C.D. Randomized rounding: a technique for provably good algorithms and algorithmic proofs. Combinatorica. 7(4):1987;365-374.
20. A. Sebö, Integer plane multicommodity flows with a bounded number of demands, Tech. Report, OR-885340, Research Institute for Discrete Mathematics, University of Bonn, Germany, 1988.
21. J. Spencer, Ten Lectures on the Probabilistic Method, SIAM, Philadelphia, 1987.
22. Srivastav A., Stangier P. Algorithmic Chernoff-Hoeffding inequalities in integer programming. Random Struct. Algorithms. 8(1):1996;27-58.
23. Tardos E. A strongly polynomial algorithm to solve combinatorial linear programs. Oper. Res. 34:1986;250-256.
24. Wagner D., Weihe K. A linear-time algorithm for edge-disjoint paths in planar graphs. Combinatorica. 15(1):1995;135-150.