Solution of the optimal assignment problem by diagonal scaling algorithms

Meisam Sharify; Stéphane Gaubert; Laura Grigori

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arXiv · 1104.3830

Solution of the optimal assignment problem by diagonal scaling algorithms

Meisam Sharify·Stéphane Gaubert·Laura Grigori

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Abstract

We show that a solution of the optimal assignment problem can be obtained as the limit of the solution of an entropy maximization problem, as a deformation parameter tends to infinity. This allows us to apply entropy maximization algorithms to the optimal assignment problem. In particular, the Sinkhorn algorithm leads to a parallelizable method, which can be used as a preprocessing to handle large dense optimal assignment problems. This parallel preprocessing allows one to delete entries which do not belong to optimal permutations, leading to a reduced instance which becomes solvable with limited memory requirements.

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Meisam Sharify, Stéphane Gaubert, Laura Grigori. 2011-04-19. Solution of the optimal assignment problem by diagonal scaling algorithms. https://arxiv.org/abs/1104.3830

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