5 citations · 9 across the 12 of their papers we have counts for
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Note on Minkowski Summation and Unimodularity in Discrete Convex Analysis
Kazuo Murota, Akihisa Tamura
This short note gives an elementary alternative proof for a theorem of Danilov and Koshevoy on Minkowski summation and unimodularity in discrete convex analysis. It is intended to…
Towards Optimal Subsidy Bounds for Envy-freeable Allocations
Yasushi Kawase, Kazuhisa Makino, Hanna Sumita +2
We study the fair division of indivisible items with subsidies among agents, where the absolute marginal valuation of each item is at most one. Under monotone valuations (where…
Decomposition of an Integrally Convex Set into a Minkowski Sum of Bounded and Conic Integrally Convex Sets
Kazuo Murota, Akihisa Tamura
Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of…
Shapley-Folkman-type Theorem for Integrally Convex Sets
Kazuo Murota, Akihisa Tamura
The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This p…