Both the difference and ratio versions of minimizing the utility gap across agents in a many-to-many stable matching are solvable in O(n⁴ + n²T_v) time via rotation-poset chain structure and sliding-window feasibility testing.
A combinatorial algorithm minimizing submodular functions in strongly polynomial time.Journal of Combinatorial Theory, Series B, 80(2):346–355, 2000
2 Pith papers cite this work, alongside 680 external citations. Polarity classification is still indexing.
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Presents a polynomial-time s-t cut algorithm for minimum Riesz s-energy k-subset selection on ordered 1D points via Monge property and submodularity, extending to ℓ1-staircases.
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Stable Matchings with Minimum Utility Gap
Both the difference and ratio versions of minimizing the utility gap across agents in a many-to-many stable matching are solvable in O(n⁴ + n²T_v) time via rotation-poset chain structure and sliding-window feasibility testing.
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Polynomial-Time Riesz-Energy Subset Selection for Ordered Point Sets on Lines and $\ell_1$-Staircases
Presents a polynomial-time s-t cut algorithm for minimum Riesz s-energy k-subset selection on ordered 1D points via Monge property and submodularity, extending to ℓ1-staircases.