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A Strongly Polynomial Algorithm for a Class of Minimum-Cost Flow Problems with Separable Convex Objectives [PDF]
SIAM Journal on Computing, 2016 A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective $\sum_{ij\in E}C_{ij}(f_{ij})$ over feasible flows $f$, where on every arc $ij$ of the network, $C_{ij}$ is a convex function.
László A Vegh
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A new strongly polynomial dual network simplex algorithm
Mathematical Programming, 1997This paper presents a new dual network simplex algorithm for the minimum cost network flow problem. The algorithm works directly on the original capacitated network and runs in O(mn(m + n log n) log n) time for the network with n nodes and m arcs. This complexity is better than the complexity of Orlin, Plotkin and Tardos' (1993) dual network simplex ...
Armstrong, Ronald D., Jin, Zhiying
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A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM, 2001This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question posed in 1981 by Grötschel, Lovász, and Schrijver. The algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter.
Satoru Iwata 0001 +2 more
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An Oracle Strongly Polynomial Algorithm for Bottleneck Expansion Problems
Optimization Methods and Software, 2002Let E = { e 1 , e 2 , , e n } be a finite set and $\cal F $ be a family of subsets of E . For each element e i in E , c i is a given capacity and w i is the cost of increasing capacity c i by one unit. The problem is how to expand the capacities of elements in E so that the capacity of $\cal F $ is as large as possible, subject to a given budget ...
Jianzhong Zhang 0001, Zhenhong Liu
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A strongly polynomial algorithm for the minimum maximum flow degree problem
Operations Research Letters, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Manoel B. Campêlo, Jhonata A. S. Matias
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A strongly polynomial algorithm for bimodular integer linear programming
Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, 2017We present a strongly polynomial algorithm to solve integer programs of the form max{cT x: Ax≤ b, xeℤn }, for AeℤmXn with rank(A)=n, be≤m, ce≤n, and where all determinants of (nXn)-sub-matrices of A are bounded by 2 in absolute value. In particular, this implies that integer programs max{cT x : Q x≤ b, xeℤ≥0n}, where Qe ℤmXn has the property that all ...
Artmann, Stephan +2 more
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A strongly polynomial minimum cost circulation algorithm
Combinatorica, 1985A new algorithm is presented for the minimum cost circulation problem. The algorithm is strongly polynomial, that is, the number of arithmetic operations is polynomial in the number of nodes, and is independent of both costs and capacities.
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Balanced network flows. III. Strongly polynomial augmentation algorithms
Networks, 1999For Parts I and II, see ibid. 33, 1-28, 29-41 (1999; Zbl 0999.90005 and Zbl 0999.90006). In this paper strongly polynomial augmentation algorithms for the maximum balanced flow problem are discussed. These algorithms use a double depth first search procedure.
Fremuth-Paeger, Christian +1 more
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A strongly polynomial Contraction-Expansion algorithm for network flow problems
Computers & Operations Research, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jean Bertrand Gauthier +2 more
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Some LCPs solvable in strongly polynomial time with Lemke’s algorithm
Mathematical Programming, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ilan Adler +2 more
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