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String Diagram of Optimal Transports

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arxiv 2408.08550 v2 pith:EWIPMORI submitted 2024-08-16 cs.AI cs.NAmath.NAmath.OC

classification cs.AIcs.NAmath.NAmath.OC
keywords hierarchicaloptimalstringalgorithmcostdiagramsframeworkmatrices
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We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient synthesis of optimal hierarchical transportation plans. Our approach uses algebraic compositions of cost matrices to effectively model hierarchical structures. We also study an adversarial situation with multiple choices in the cost matrices, where we present a polynomial-time algorithm for a relaxation of the problem. Experimental results confirm the efficiency and performance advantages of our proposed algorithm over the naive method.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Sinkhorn Algorithm for Sequentially Composed Optimal Transports

    cs.DS 2024-12 accept novelty 6.0 of 10

    A Sinkhorn-type algorithm for sequentially composed optimal transport is shown to converge exponentially in the Hilbert metric and, for two stages, to have near-linear worst-case time in the plan size.

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