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Strongly Polynomial Algorithms for the Unsplittable Flow Problem
Lecture Notes in Computer Science, 2001 We provide the first strongly polynomial algorithms with the best approximation ratio for all three variants of the unsplittable flow problem (UFP). In this problem we are given a (possibly directed) capacitated graph with n vertices and m edges, and a set of terminal pairs each with its own demand and profit.
Yossi Azar, Azar Yossi
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Strongly Polynomial Algorithms for the High Multiplicity Scheduling Problem
Operations Research, 1991A high multiplicity scheduling problem consists of many jobs which can be partitioned into relatively few groups, where all the jobs within each group are identical. Polynomial, and even strongly polynomial, algorithms for the standard scheduling problem, in which all jobs are assumed to be distinct, become exponential for the corresponding high ...
Dorit S Hochbaum, Ron Shamir
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A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs
Operations Research, 1986Khachiyan, and recently Karmarkar, gave polynomial algorithms to solve the linear programming problem. These algorithms have a small theoretical drawback; namely, the number of arithmetic steps depends on the size of the input numbers. We present a polynomial linear programming algorithm whose number of arithmetic steps depends only on the size of the
Eva Tardos
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Strongly Polynomial Algorithms for Transient and Average-Cost MDPs
ACM SIGMETRICS Performance Evaluation Review, 2017 This paper considers transient total-cost MDPs with transition rates whose values may be greater than one, and average-cost MDPs satisfying the condition that the expected time to hit a certain state from any initial state and under any stationary policy is bounded above by a constant. Linear programming formulations for such MDPs are provided that are
Eugene A. Feinberg, Jefferson Huang
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A Strongly Polynomial Algorithm for Minimum Cost Submodular Flow Problems
Mathematics of Operations Research, 1989The only known strongly polynomial algorithm for solving minimum cost submodular flow problems is due to Frank and Tardos (Frank, A., É. Tardos. 1985. An application of the simultaneous approximation in combinatorial optimization. Report No. 85375, Institut für Ökonometrie und Operations Research, Bonn, May.) and is based on the simultaneous ...
Satoru Fujishige
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Modified policy iteration algorithms are not strongly polynomial for discounted dynamic programming [PDF]
Operations Research Letters, 2014 International audienceThis note shows that the number of arithmetic operations required by any member of a broad class of optimistic policy iteration algorithms to solve a deterministic discounted dynamic programming problem with three states and four ...
Eugene A Feinberg +2 more
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A strongly polynomial algorithm for the transportation problem
Mathematical Programming, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Peter Kleinschmidt, Heinz Schannath
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Two strongly polynomial cut cancelling algorithms for minimum cost network flow
Discrete Applied Mathematics, 1993 We present two new strongly polynomial algorithms for the minimum cost network flow problem (MCNF). They are dual algorithms based on cancelling positive augmenting cuts, which are the duals of negative augmenting cycles.
Ervolina, Thomas R., McCormick, S.Thomas
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Strongly polynomial algorithm for two special minimum concave cost network flow problems
Optimization, 1995 We consider two special cases of the Minimum Concave Cost Network Flow Problem (MCCNFP);the single source uncapacitated MCCNFP where all arc costs, except two, are linear and the uncapacitated MCCNFP with 2 sources and 1 nonlinear arc cost.
A Migdalas
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A Strongly Polynomial Algorithm for a Special Class of Linear Programs
Operations Research, 1991We extend the list of linear programming problems that are known to be solvable in strongly polynomial time to include a class of LPs which contains special cases of the generalized transshipment problem. The result is facilitated by exploiting some special properties associated with Leontief substitution systems and observing that a feasible solution
Ilan Adler, Steven Cosares
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