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...

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...

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 <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>

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...