We describe a new dual algorithm for the minimum cost flow problem. It can be regarded as a variation of the best known strongly polynomial minimum cost flow algorithm, due to Orlin. Indeed we obtain the same running time of O(m log m(m+n log n)), where n and m denote the number of vertices and...

The minimum cost flow problem is to determine a least cost shipment of a commodity through a network G = (N, A) in order to satisfy demands at certain nodes from available supplies at other nodes. In this paper, we study a variant of the minimum cost flow problem where we are given a set R...

Jiang et al. proposed an algorithm to solve the inverse minimum cost flow problems under the bottleneck-type weighted Hamming distance [Y. Jiang, L. Liu, B. Wuc, E. Yao, Inverse minimum cost flow problems under the weighted Hamming distance, European Journal of Operational Research 207 (2010)...

Given an undirected network G(V, E, c) and a perfect matching M <Superscript>0</Superscript>, the inverse maximum perfect matching problem is to modify the cost vector as little as possible such that the given perfect matching M <Superscript>0</Superscript> can form a maximum perfect matching. The modification can be measured by different norms. In...</superscript></superscript>

LetM <Subscript>1</Subscript> andM <Subscript>2</Subscript> be matroids onS,B be theirk-element common independent set, andw a weight function onS. Given two functionsb ≥ 0 andc ≥ 0 onS, the Inverse Matroid Intersection Problem (IMIP) is to determine a modified weight functionw′ such that (a)B becomes a maximum weight common...</subscript></subscript>

Given a networkN=(V,A,c), a sources εV, a. sinkt εV and somes —t cuts and suppose each element of the capacity vectorc can be changed with a cost proportional to the changes, the inverse problem of minimum cuts we study here is to change the original capacities with the least total cost...

LetM 1 andM 2 be matroids onS,B be theirk-element common independent set, andw a weight function onS. Given two functionsb ≥ 0 andc ≥ 0 onS, the Inverse Matroid Intersection Problem (IMIP) is to determine a modified weight functionw′ such that (a)B becomes a maximum weight common...

Given a networkN=(V,A,c), a sources εV, a. sinkt εV and somes —t cuts and suppose each element of the capacity vectorc can be changed with a cost proportional to the changes, the inverse problem of minimum cuts we study here is to change the original capacities with the least total cost...

An inverse optimization problem is defined as follows. Let S denote the set of feasible solutions of an optimization problem P, let c be a specified cost (capacity) vector, and x0 ∈ S. We want to perturb the cost (capacity) vector c to d so that x0 is an optimal solution of P with respect to...