Bounds for α-optimal partitioning of a measurable space based on several efficient partitions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:425

Article

Dall'Aglio, Marco¹  Di Luca, Camilla¹ 

[1] LUISS Univ, Rome, Italy

关键词: Dvoretzky-Wald-Wolfowitz;    convexity theorem;    Cake-cutting problems;    Fair division;    Optimal partitioning;    Convex analysis;    Maxmin solution;   

DOI  :  10.1016/j.jmaa.2014.12.056

来源: Elsevier

【 摘 要 】

We provide a two-sided inequality for the alpha-optimal partition value of a measurable space according to a finite number of nonatomic finite measures. The result extends and often improves Legut [Inequalities for alpha-optimal partitioning of a measurable space, Proc. Amer. Math. Soc. 104 (1988)] since the bounds are obtained considering several partitions that maximize the weighted sum of the partition values with varying weights, instead of a single one. Furthermore, we show conditions that make these bounds sharper. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free