General restricted inverse assignment problems under l1 and l∞ norms

In this paper, we study the general restricted inverse assignment problems, in which we can only change the costs of some specific edges of an assignment problem as less as possible, so that a given assignment becomes the optimal one. Under l 1 norm, we formulate this problem as a linear programming...

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Vydané v:Journal of combinatorial optimization Ročník 44; číslo 3; s. 2040 - 2055
Hlavní autori: Wang, Qin, Yang, Tianyu, Wu, Longshu
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.10.2022
Springer Nature B.V
Predmet:
Combinatorial analysis
Combinatorics
Convex and Discrete Geometry
Linear programming
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Minimum cost
Norms
Operations research
Operations Research/Decision Theory
Optimization
Polynomials
Search algorithms
Theory of Computation
Strongly polynomial complexity
Restricted inverse problem
Assignment problem
Combinatorial algorithm
ISSN:1382-6905, 1573-2886
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Shrnutí:In this paper, we study the general restricted inverse assignment problems, in which we can only change the costs of some specific edges of an assignment problem as less as possible, so that a given assignment becomes the optimal one. Under l 1 norm, we formulate this problem as a linear programming. Then we mainly consider two cases. For the case when the specific edges are only belong to the given assignment, we show that this problem can be reduced to some variations of the minimum cost flow problems. For the case when every specific edge does not belong to the given assignment, we show that this problem can be solved by a minimum cost circulation problem. In both cases, we present some combinatorial algorithms which are strongly polynomial. We also study this problem under the l ∞ norm. We propose a binary search algorithm and prove that the optimal solution can be obtained in polynomial time.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-020-00577-1