A Linear Programming Approach for Maximum Integral Multiflow and Minimum Multicut Problems in Unrestricted Network | IEEE Conference Publication | IEEE Xplore

A Linear Programming Approach for Maximum Integral Multiflow and Minimum Multicut Problems in Unrestricted Network


Abstract:

The minimum cut and maximum flow problems form a well-known pair of dual problems providing a min-max relation. Similarly, the continuous relaxation of the minimum multic...Show More

Abstract:

The minimum cut and maximum flow problems form a well-known pair of dual problems providing a min-max relation. Similarly, the continuous relaxation of the minimum multicut problem is the linear dual of a continuous maximum integral multiflow problem. However, both integer multiflow and multicut problems are known to be NP (Nondeterministic Polynomial)-hard and Max SNP (Strongly Nondeterministic Polynomial)-hard problems in unrestricted graphs/networks. In this paper, we formulate the maximum integral multiflow problem as a linear programming model, and propose a method to obtain a minimum multicut set. The proposed model is solved by a commercial optimization toolbox, CPLEX, with promising results, and so the efficiency and effectiveness of the approach are confirmed.
Date of Conference: 30 August 2023 - 01 September 2023
Date Added to IEEE Xplore: 16 October 2023
ISBN Information:
Conference Location: Birmingham, United Kingdom

References

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