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dc.contributor.authorDelon, Julie
HAL ID: 6864
dc.contributor.authorSalomon, Julien
HAL ID: 738224
dc.contributor.authorSobolevski, Andrei
dc.subjectMonge-Kantorovich problemen
dc.subjectAubry-Mather (weak KAM) theoryen
dc.subjectOptimization and Controlen
dc.titleFast Transport Optimization for Monge Costs on the Circleen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherIndependent University of Moscow, Moscow;Russie
dc.description.abstractenConsider the problem of optimally matching two measures on the circle, or equivalently two periodic measures on the real line, and suppose the cost of matching two points satisfies the Monge condition. We introduce a notion of locally optimal transport plan, motivated by the weak KAM (Aubry-Mather) theory, and show that all locally optimal transport plans are conjugate to shifts. This theory is applied to a transportation problem arising in image processing: for two sets of point masses, both of which have the same total mass, find an optimal transport plan with respect to a given cost function that satisfies the Monge condition. For the case of N real-valued point masses we present an O(N log epsilon) algorithm that approximates the optimal cost within epsilon; when all masses are integer multiples of 1/M, the algorithm gives an exact solution in O(N log M) operations.en
dc.relation.isversionofjnlnameSIAM Journal on Applied Mathematics
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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