Efficient dual simplex algorithms for the assignment problem
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Efficient algorithms based upon Balinski's signature method are described for solving then × n assignment problem and are shown to have computational bounds of O(n3) space and O(mn + n2 logn) time in the worst case.Abstract:
Efficient algorithms based upon Balinski's signature method are described for solving then × n assignment problem. These algorithms are special variants of the dual simplex method and are shown to have computational bounds of O(n3). Variants for solving sparse assignment problems withm arcs that require O(m) space and O(mn + n2 logn) time in the worst case are also presented.read more
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A shortest augmenting path algorithm for dense and sparse linear assignment problems
R. Jonker,A. Volgenant +1 more
TL;DR: A shortest augmenting path algorithm for the linear assignment problem that contains new initialization routines and a special implementation of Dijkstra's shortest path method is developed.
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The auction algorithm: a distributed relaxation method for the assignment problem
TL;DR: A massively parallelizable algorithm for the classical assignment problem was proposed in this article, where unassigned persons bid simultaneously for objects thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder.
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Inverse Optimization
Ravindra K. Ahuja,James B. Orlin +1 more
TL;DR: In inverse optimization problems defined as follows, it is proved that if the problemP is a linear programming problem, then its inverse problem under theL1 as well asL8 norm is also alinear programming problem and inverse versions ofP under the L1 andL8 norms are also polynomially solvable.
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Efficient algorithms for finding maximum matching in graphs
TL;DR: The techniques used for designing the most efficient algorithms for finding a maximum cardinality or weighted matching in (general or bipartite) graphs are surveyed.
References
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Journal ArticleDOI
The Hungarian method for the assignment problem
TL;DR: This paper has always been one of my favorite children, combining as it does elements of the duality of linear programming and combinatorial tools from graph theory, and it may be of some interest to tell the story of its origin this article.
Book
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Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
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An $n^{5/2} $ Algorithm for Maximum Matchings in Bipartite Graphs
John E. Hopcroft,Richard M. Karp +1 more
TL;DR: This paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to $(m + n)\sqrt n $.
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Fibonacci heaps and their uses in improved network optimization algorithms
TL;DR: Using F-heaps, a new data structure for implementing heaps that extends the binomial queues proposed by Vuillemin and studied further by Brown, the improved bound for minimum spanning trees is the most striking.