Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T10:55:58.981Z Has data issue: false hasContentIssue false
  • English
  • Français

The inverse maximum flow problem considering l ∞ norm

Published online by Cambridge University Press:  20 August 2008

Adrian Deaconu
Adrian Deaconu*
Affiliation:
University “Transilvania” of Brasov, Faculty of Mathematics and Informatics, Theoretical Computer Science Departement, str. Iuliu Maniu 50, Brasov, Romania; [email protected]
Get access

Abstract

The problem is to modify the capacities of the arcs from a network so that a given feasible flow becomes a maximum flow and the maximum change of the capacities on arcs is minimum. A very fast O(m⋅log(n)) time complexity algorithm for solving this problem is presented, where m is the number of arcs and n is the number of nodes of the network. The case when both, lower and upper bounds of the flow can be modified so that the given feasible flow becomes a maximum flow is also discussed. The algorithm proposed can be adapted to solve this problem, too. The inverse minimum flow problem considering l ∞ norm is also studied.

Keywords

Inverse combinatorial optimizationmaximum flowstrongly polynomial time complexity.
Type
Research Article
Information
RAIRO - Operations Research , Volume 42 , Issue 3 , July 2008 , pp. 401 - 414
Copyright
© EDP Sciences, ROADEF, SMAI, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

R.K. Ahuja, T.L. Magnanti and J.B. Orlin, Network Flows. Theory, Algorithms and Applications, Prentice Hall, Englewood Cliffs, NJ (1993).
R.K. Ahuja and J.B. Orlin, Combinatorial Algorithms for Inverse Network Flow Problems, Networks (2002).
R.K. Ahuja and J.B. Orlin, Inverse Optimization, Working Paper, Sloan School of Management, MIT, Cambridge, MA (1998).
E. Ciurea and L. Ciupala, Sequential and Parallel Algorithms for Minimum Flows, J. Appl. Math. Comput. 15 (2004) 53–75. CrossRef
E. Ciurea and A. Deaconu, Inverse Minimum Flow Problem, J. Appl. Math. Comp., Korea 23 (2007) 193–203.
A. Deaconu, The Inverse Maximum Flow Problem with Lower and Upper Bounds for the Flow, to appear in YUJOR 18 (2008).
A. Deaconu, A Cardinality Inverse Maximum Flow Problem, Scientific Annals of Computer Science XVI (2006) 51–62.
C. Heuberger, Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results, J. Combin. Optim. 8 (2004) 329–361. CrossRef
L. Liu and J. Zhang, Inverse Maximum Flow Problems under Weighted Hamming Distance, J. Combin. Optim. 12 (2006) 395–408. CrossRef
P.T. Sokkalingam, R.K. Ahuja and J.B. Orlin, Solving Inverse Spanning Tree Problems through Network Flow Techniques, Oper. Res. 47 (1999) 291–298.
C. Yang and X. Chen, An Inverse Maximum Capacity Path Problem with Lower Bound Constraints, Acta Math. Sci., Ser. B 22 (2002) 207–212.
C. Yang, J. Zhang and Z. Ma, Inverse Maximum Flow and Minimum Cut Problems, Optimization 40 (1997) 147–170.
J. Zhang and C. Cai, Inverse Problems of Minimum Cuts, ZOR-Math. Methods Oper. Res. 47 (1998) 51–58.