Given a network G(V, A, u) with two specific nodes, a source node s and a sink node t, the reverse maximum flow problem is to increase the capacity of some arcs (i, j) as little as possible under bound constraints on the modifications so that the maximum flow value from s to t in the modified network is lower bounded by a prescribed value v^{0}. In this paper, we study the reverse maximum flow problem when the capacity modifications are measured by the weighted Chebyshev distance. We present an efficient algorithm to solve the problem in two phases. The first phase applies the binary search technique to find an interval containing the optimal value. The second phase uses the discrete type Newton method to obtain exactly the optimal value. Finally, some computational experiments are conducted to observe the performance of the proposed algorithm.
Accepted:
DOI: 10.1051/ro/2017088
Keywords: Maximum flow problem, reverse problem, Chebyshev distance, network design, Newton method, binary search
@article{RO_2018__52_4-5_1107_0, author = {Tayyebi, Javad and Mohammadi, Abumoslem and Kazemi, Seyyed Mohammad Reza}, title = {Reverse maximum flow problem under the weighted {Chebyshev} distance}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {1107--1121}, publisher = {EDP-Sciences}, volume = {52}, number = {4-5}, year = {2018}, doi = {10.1051/ro/2017088}, mrnumber = {3878615}, zbl = {1411.90346}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ro/2017088/} }
TY - JOUR AU - Tayyebi, Javad AU - Mohammadi, Abumoslem AU - Kazemi, Seyyed Mohammad Reza TI - Reverse maximum flow problem under the weighted Chebyshev distance JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 1107 EP - 1121 VL - 52 IS - 4-5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2017088/ DO - 10.1051/ro/2017088 LA - en ID - RO_2018__52_4-5_1107_0 ER -
%0 Journal Article %A Tayyebi, Javad %A Mohammadi, Abumoslem %A Kazemi, Seyyed Mohammad Reza %T Reverse maximum flow problem under the weighted Chebyshev distance %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 1107-1121 %V 52 %N 4-5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2017088/ %R 10.1051/ro/2017088 %G en %F RO_2018__52_4-5_1107_0
Tayyebi, Javad; Mohammadi, Abumoslem; Kazemi, Seyyed Mohammad Reza. Reverse maximum flow problem under the weighted Chebyshev distance. RAIRO - Operations Research - Recherche Opérationnelle, Volume 52 (2018) no. 4-5, pp. 1107-1121. doi : 10.1051/ro/2017088. http://archive.numdam.org/articles/10.1051/ro/2017088/
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