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Banikhademi, H., Salehi Fathabadi, H.. (1395). Inverse Maximum Dynamic Flow Problem under the Sum-Type Weighted Hamming Distance. , 2(شماره 6), 101-111.
H. Banikhademi; H. Salehi Fathabadi. "Inverse Maximum Dynamic Flow Problem under the Sum-Type Weighted Hamming Distance". , 2, شماره 6, 1395, 101-111.
Banikhademi, H., Salehi Fathabadi, H.. (1395). 'Inverse Maximum Dynamic Flow Problem under the Sum-Type Weighted Hamming Distance', , 2(شماره 6), pp. 101-111.
Banikhademi, H., Salehi Fathabadi, H.. Inverse Maximum Dynamic Flow Problem under the Sum-Type Weighted Hamming Distance. , 1395; 2(شماره 6): 101-111.

Inverse Maximum Dynamic Flow Problem under the Sum-Type Weighted Hamming Distance

Journal of New Researches in Mathematics
مقاله 8، دوره 2، شماره 6، بهمن 2016، صفحه 101-111  XML اصل مقاله (2.21 M)
نوع مقاله: research paper
نویسندگان
H. Banikhademi* 1؛ H. Salehi Fathabadi* 2
1Phd Student of Mathematics, Karaj Branch, Isalmic Azad University, Karaj, Iran
2Department of Mathematics, Karaj Branch, Isalmic Azad University, Karaj, Iran
چکیده
Inverse maximum flow (IMDF), is among the most important problems in the field of
dynamic network flow, which has been considered the Euclidean norms measure in previous
researches. However, recent studies have mainly focused on the inverse problems under the
Hamming distance measure due to their practical and important applications. In this paper,
we studies a general approach for handling the inverse maximum dynamic flow problem
under the weighted sum-type Hamming distance. We assume that a dynamic network flow,
and a desired feasible dynamic flow on the network is given. We try to adjust the current arc
capacity vector to maximize the dynamic flow and minimize the changes. The motivation
for this study stems from the Hamming distance that is made practically important in the
situation where we only care about the change, disregarding its magnitude. In this paper,
first we prove some preliminary results, then we show that this problem (IMDF) can be
transformed to a minimum dynamic cut problem. So, we proposed a combinatorial
algorithm for solving the IMDF in strongly polynomial time. Ultimately, the proposed
algorithm, is illustrated by a numerical example on a dynamic network.
کلیدواژه‌ها
Dynamic network flows؛ Inverse Optimization؛ Euclidean norms؛ Hamming distance
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