Zobrazeno 1 - 10
of 128
pro vyhledávání: '"Tamura, Akihisa"'
Autor:
Murota, Kazuo, Tamura, Akihisa
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 disseminate this fundamental theorem and make its proof accessible to
Externí odkaz:
http://arxiv.org/abs/2312.01822
We study the fair division of indivisible items with subsidies among $n$ agents, where the absolute marginal valuation of each item is at most one. Under monotone valuations (where each item is a good), Brustle et al. (2020) demonstrated that a maxim
Externí odkaz:
http://arxiv.org/abs/2308.11230
Autor:
Murota, Kazuo, Tamura, Akihisa
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 discrete sets in discrete convex analysis, such as integrally convex
Externí odkaz:
http://arxiv.org/abs/2306.09072
Autor:
Murota, Kazuo, Tamura, Akihisa
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 paper establishes similar theorems for integrally convex sets, L-natura
Externí odkaz:
http://arxiv.org/abs/2305.15125
Autor:
Murota, Kazuo, Tamura, Akihisa
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on integrally conve
Externí odkaz:
http://arxiv.org/abs/2211.10912
Autor:
Murota, Kazuo, Tamura, Akihisa
Publikováno v:
In Discrete Applied Mathematics 15 January 2025 360:42-50
Autor:
Murota, Kazuo, Tamura, Akihisa
Discrete Fenchel duality is one of the central issues in discrete convex analysis. The Fenchel-type min-max theorem for a pair of integer-valued M-natural-convex functions generalizes the min-max formulas for polymatroid intersection and valuated mat
Externí odkaz:
http://arxiv.org/abs/2108.10502
Autor:
Goko, Hiromichi, Igarashi, Ayumi, Kawase, Yasushi, Makino, Kazuhisa, Sumita, Hanna, Tamura, Akihisa, Yokoi, Yu, Yokoo, Makoto
Publikováno v:
In Games and Economic Behavior March 2024 144:49-70
Autor:
Goko, Hiromichi, Igarashi, Ayumi, Kawase, Yasushi, Makino, Kazuhisa, Sumita, Hanna, Tamura, Akihisa, Yokoi, Yu, Yokoo, Makoto
The notion of \emph{envy-freeness} is a natural and intuitive fairness requirement in resource allocation. With indivisible goods, such fair allocations are unfortunately not guaranteed to exist. Classical works have avoided this issue by introducing
Externí odkaz:
http://arxiv.org/abs/2105.01801
Autor:
Tamura, Akihisa, Tsurumi, Kazuya
For continuous functions, midpoint convexity characterizes convex functions. By considering discrete versions of midpoint convexity, several types of discrete convexities of functions, including integral convexity, L$^\natural$-convexity and global/l
Externí odkaz:
http://arxiv.org/abs/2001.11676