On a dual network exterior point simplex type algorithm and its computational behavior

RAIRO - Operations Research

Volumn 46, Issue 3, 2012, Pages 211-234

  Geranis, George ^a   Paparrizos, Konstantinos ^a   Sifaleras, Angelo ^a  

^a UNIVERSITY OF MACEDONIA   (Greece)

Author keywords

Dual network exterior point simplex algorithm; Minimum cost network flow problem; Network flows

Indexed keywords

FORESTRY; LINEAR PROGRAMMING;

COMPUTATIONAL STUDIES; FEASIBLE SOLUTION; MATHEMATICAL PROOF; MINIMUM COST NETWORK FLOW PROBLEM; NETWORK FLOW PROBLEMS; NETWORK FLOWS; NUMBER OF ITERATIONS; SIMPLEX ALGORITHM;

TREES (MATHEMATICS);

ALGORITHMS; COSTS; FORESTRY; MATHEMATICS; PROBLEM SOLVING; TREES;

EID: 84876862661     PISSN: 03990559     EISSN: 28047303     Source Type: Journal    
DOI: 10.1051/ro/2012015     Document Type: Article

References (32)

1. R.K. Ahuja, T.L. Magnanti and J.B. Orlin, Network flows : theory, algorithms and applications. Prentice Hall, Englewood Cliffs, NJ (1993).
2. R.K. Ahuja, T.L. Magnanti, J.B. Orlin and M. Reddy, Applications of network optimization. Handbooks of Operations Research and Management Science 7 (1995) 1-83.
3. D. Andreou, K. Paparrizos, N. Samaras and A. Sifaleras, Visualization of the network exterior primal simplex algorithm for the minimum cost network flow problem. Oper. Res. 7 (2007) 449-464.
4. Th. Baloukas, K. Paparrizos and A. Sifaleras, An animated demonstration of the uncapacitated network simplex algorithm. ITE 10 (2009) 34-40.
5. D.P. Bertsekas and P. Tseng, RELAX-IV : A faster version of the RELAX code for solving minimum cost flow problems. Technical Report, Massachusetts Institute of Technology, Laboratory for Information and Decision Systems (1994).
6. S. Chakraborty and P.P. Choudhury, A statistical analysis of an algorithm's complexity. Appl. Math. Lett. 13 (2000) 121-126.
7. M. Coffin and M.J. Saltzman, Statistical Analysis of computational tests of algorithms and heuristics. INFORMS J. Comput. 12 (2000) 24-44.
8. C. Cotta and P. Moscato, A mixed evolutionary-statistical analysis of an algorithm's complexity. Appl. Math. Lett. 16 (2003) 41-47.
9. T.R. Ervolina and S.T. McCormick, Two strongly polynomial cut canceling algorithms for minimum cost network flow. Discr. Appl. Math. 46 (1993) 133-165.
10. M. Fredman and R. Tarjan, Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM 34 (1987) 596-615.
11. K. Fukuda and T. Terlaky, Criss-cross methods : a fresh view on pivot algorithms. Math. Program. 79 (1997) 369-395.
12. G. Geranis, K. Paparrizos and A. Sifaleras, A dual exterior point simplex type algorithm for the minimum cost network flow problem. Yugosl. J. Oper. Res. 19 (2009) 157-170.
13. G. Geranis, K. Paparrizos and A. Sifaleras, On the Computational Behavior of a Dual Network Exterior Point Simplex Algorithm for the Minimum Cost Network Flow Problem, in Proceedings of the International Network Optimization Conference (INOC 2009). Pisa, Italy (2009).
14. F. Glover, D. Klingman and A. Napier, Basic dual feasible solutions for a class of generalized networks. Oper. Res. 20 (1972) 126-136.
15. F. Glover, D. Karney and D. Klingman, The augmented predecessor index method for locating stepping stone paths and assigning dual prices in distribution problems. Transp. Sci. 6 (1972) 171-180.
16. F. Glover, D. Klingman and N. Phillips, Network models in optimization and their applications in practice. Wiley Publications (1992).
17. A.V. Goldberg, An Efficient Implementation of a scaling minimum-cost flow algorithm. J. Algorithms 22 (1997) 1-29.
18. A. Goldberg, M. Grigoriadis and R.E. Tarjan, Use of dynamic trees in a network simplex algorithm for the maximum flow problem, Math. Program. 50 (1991) 277-290.
19. M. Grigoriadis, An efficient implementation of the network simplex method. Math. Program. Stud. 26 (1984) 83-111.
20. J. Hultz and D. Klingman, An advanced dual basic feasible solution for a class of capacitated generalized networks. Oper. Res. 24 (1976) 301-313.
21. J. Kennington and R. Helgason, Algorithms for network programming. Wiley, New York (1980).
22. D. Klingman, A. Napier and J. Stutz, NETGEN : a program for generating large scale capacitated assignment, transportation, and minimum cost flow networks. Manag. Sci. 20 (1974) 814-821.
23. I. Maros, A practical anti-degeneracy row selection technique in network linear programming. Ann. Oper. Res. 47 (1993) 431-442.
24. C.C. McGeoch, Toward an experimental method for algorithm simulation. INFORMS J. Comput. 8 (1996) 1-15.
25. R. Nance, R. Moose and R. Foutz, A statistical technique for comparing heuristics : an example from capacity assignment strategies in computer network design. Commun. ACM 30 (1987) 430-442.
26. J.B. Orlin, Genuinely polynomial simplex and non-simplex algorithms for the minimum cost flow problem. Technical Report No. 1615-84, Sloan School of Management, M.I.T., Cambridge, MA (1984).
27. K. Paparrizos, N. Samaras and A. Sifaleras, An exterior simplex type algorithm for the minimum cost network flow problem. Comput. Oper. Res. 36 (2009) 1176-1190.
28. M. Resende and G. Veiga, An efficient implementation of a network interior point method, in Network flows and matching : first DIMACS implementation challenge 12, edited by D.S. Johnson and C.C. McGeoch. DIMACS series in discrete mathematics and theoretical computer science, American Mathematical Society, Providence, Rhode Island (1993) 299-348.
29. R.E. Tarjan, Dynamic trees as search trees via Euler tours, applied to the network simplex algorithm. Math. Program. 78 (1997) 169-177.
30. R. Vanderbei, Linear programming : foundations and extensions, 3rd edition. Springer, New York (2007).
31. N. Zadeh, More pathological examples for network flow problems. Math. Program. 5 (1973) 217-224.
32. N. Zadeh, A bad network problem for the simplex method and other minimum cost flow algorithms. Math. Programm. 5 (1973) 255-266.