A cut-based algorithm for the nonlinear dual of the minimum cost network flow problem

Algorithmica (New York)

Volumn 39, Issue 3, 2004, Pages 189-208

  Ahuja, Ravindra K ^a   Hochbaum, Dorit S ^b   Orlin, James B ^c  

^a University of Florida   (United States)

^b DEPARTMENT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Convex integer programming; Minimum cut; Network flow; Nonlinear integer programming; Total unimodularity

Indexed keywords

COSTS; FUNCTIONS; INTEGER PROGRAMMING; NONLINEAR SYSTEMS; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING; SCHEDULING; STATISTICAL METHODS;

CONVEX INTEGER PROGRAMMING; MINIMUM CUT; NETWORK FLOW; NONLINEAR INTEGER PROGRAMMING; TOTAL UNIMODULARITY;

ALGORITHMS;

EID: 21044452195     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-004-1085-2     Document Type: Article

References (21)

1. [AHO] R. K. Ahuja, D. S. Hochbaum, and J. B. Orlin. Solving the convex cost integer dual network flow problem. Management Science, 49(7), 950-964, 2003.
2. [AMO] R. K. Ahuja, T. L. Magnanti, and J. B. Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Englewood Cliffs, NJ, 1993.
3. [BBBB] R. E. Barlow, D. J. Bartholomew, J. M. Bremer, and H. D. Brunk. Statistical Inference Under Order Restrictions. Wiley, New York, 1972.
4. [BJ] R. G. Bland and D. L. Jensen. On the computational behavior of a polynomial time network flow algorithm. Mathematical Programming, 54, 1-39.1992.
5. [CH] J. Cheriyan and T. Hagerup. A randomized maximum-flow algorithm. SIAM Journal on Computing, 24, 203-226, 1995.
6. [D] G. B. Dantzig. Linear Programming and Extensions. Princeton University Press, Princeton. NJ, 1963.
7. [GR] A. V. Goldberg and S. Rao. Beyond the flow decomposition barrier. Journal of the ACM, 45, 783-797, 1998.
8. [GT1] A. V. Goldberg and R. E. Tarjan. A new approach to the maximum flow problem. Journal of the ACM, 35, 921-940, 1988.
9. [GT2] A. V. Goldberg and R. E. Tarjan. Solving minimum cost flow problem by successive approximation. Mathematics of Operations Research, 15, 430-466, 1990.
10. [H1] D. S. Hochbaum. The pseudoflow algorithm for the maximum flow problem. Manuscript, University of California, Berkeley, CA, 1997.
11. [H2] D. S. Hochbaum. An efficient algorithm for image segmentation, Markov Random Fields and related problems. Journal of the ACM, 48(4), 686-701, 2001.
12. [H3] D.S. Hochbaum. The inverse shortest paths problem. Manuscript, University of California, Berkeley, CA, July 2001.
13. [H4] D. S. Hochbaum. Solving integer programs over monotone inequalities in three variables: a framework for half integrality and good approximations. European Journal of Operational Research, 140(2), 291-321, 2002.
14. [H5] D. S. Hochbaum. Efficient algorithms for the inverse spanning tree problem. Operations Research, 51(5), 785-797, 2003.
15. [HMNT] D. S. Hochbaum, N. Megiddo, J. Naor, and A. Tamir. Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality. Mathematical Programming, 62, 69-83, 1993.
16. [HN] D. S. Hochbaum and J. Naor. Simple and fast algorithms for linear and integer programs with two variables per inequality. SIAM Journal on Computing, 23(6), 1179-1192,1994.
17. [HQ] D. S. Hochbaum and M. Queyranne. Minimizing a convex cost closure set. SIAM Journal of Discrete Mathematics, 16(2), 192-207, 2003.
18. [HS] D. S. Hochbaum and J. G. Shanthikumar. Convex separable optimization is not much harder than linear optimization. Journal of the ACM, 37, 843-862, 1990.
19. [KM] A. V. Karzanov and S. T. McCormick. Polynomial methods for separable convex optimization in unimodular linear spaces with applications. SIAM Journal on Computing, 26(4), 1245-1275, 1997.
20. [P] J. C. Picard. Maximal closure of a graph and applications to combinatorial problems. Management Science, 22, 1268-1272, 1976.
21. [R] H. Röck. Scaling techniques for minimum cost network flows. In Discrete Structures and Algorithms, V. Pape, ed. Carl Hansen, Munich, pp. 181-191, 1980.