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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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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.
Eva Tardos
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Strongly Polynomial Algorithms for the Unsplittable Flow Problem [PDF]
, 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, Oded Regev 0001
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Strongly polynomial algorithm for a class of combinatorial LCPs
Operations Research Letters, 1987We show that an LCP with positive definite coefficient matrix can be solved in time polynomially bounded by the size of the numbers in the coefficient matrix. As a special case, we have a strongly polynomial algorithm for the problem of fitting the best convex curve to a given set of points in \(R^ 2\).
S N Kabadi
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A Strongly Polynomial Time Algorithm for Multicriteria Global Minimum Cuts [PDF]
, 2014 We investigate the bicriteria global minimum cut problem where each edge is evaluated by two nonnegative cost functions. The parametric complexity of such a problem is the number of linear segments in the parametric curve when we take all convex combinations of the criteria. We prove that the parametric complexity of the global minimum cut problem is O(
Hassene Aissi +3 more
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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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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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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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Strongly polynomial algorithm for a production-transportation problem with concave production cost [PDF]
Optimization, 1993 This paper presents a strongly polynomial algorithm for a special concave minimization problem which is a production-transportation problem involving concave production cost and linear transportation cost. The method used is characterized by a systematic
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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