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We show that Fermat–Weber problems under simplicial distances, having both sources and destinations as input, are equivalent to specific minimum cost flow problems. In particular, this enables the efficient computation of geometric medians involving Hilbert’s projective metric for a simplex.

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Simplicial Fermat–Weber Problems Are Dual to Minimum Cost Flow Problems

  • 会议论文

  • 发表日期：

    2026年

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  • Andrei Comăneci

摘要

We show that Fermat–Weber problems under simplicial distances, having both sources and destinations as input, are equivalent to specific minimum cost flow problems. In particular, this enables the efficient computation of geometric medians involving Hilbert’s projective metric for a simplex.