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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fair cake-cutting ： ウィキペディア英語版 Fair cake-cutting Fair cake-cutting is a kind of fair division problem. The problem involves a ''heterogenous'' resource, such as a cake with different toppings, that is assumed to be ''divisible'' – it is possible to cut arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who have different preferences over different parts of the cake, i.e., some people prefer the chocolate toppings, some prefer the cherries, some just want as large a piece as possible, etc. The division should be subjectively fair, i.e., each person should receive a piece that he/she believes to be a fair share. The "cake" is only a metaphor; procedures for fair cake-cutting can be used to divide various kinds of resources, such as land estates, advertisement space or broadcast time. The cake-cutting problem was introduced by Hugo Steinhaus after World War II and is still the subject of intense research in mathematics, computer science, economics and political science. == Assumptions == There is a cake ''C'', which is usually assumed to be either a finite 1-dimensional segment, a 2-dimensional polygon or a finite subset of the multidimensional Euclidean plane R''d''. There are ''n'' people with equal rights to ''C''.〔I.e. there is no dispute over the rights of the people – the only problem is how to divide the cake such that each person receives a fair share.〕 ''C'' has to be divided to ''n'' disjoint subsets, such that each person receives a disjoint subset. The piece allocated to person ''i'' is called ''P''''i'', and $C\; =\; P\_1\; \backslash sqcup\; \backslash cdots\; \backslash sqcup\; P\_n$. Each person should get a piece with a "fair" value. Fairness is defined based on subjective value functions. Each person ''i'' has a subjective value function ''V''''i'' which maps subsets of ''C'' to numbers. All value functions are assumed to be absolutely continuous with respect to the length, area or (in general) Lebesgue measure. This means that there are no "atoms" – there are no singular points to which one or more agents assign a positive value, so all parts of the cake are divisible. Additionally, in some cases the value functions are assumed to be sigma additive (the value of a whole is equal to the sum of the values of its parts). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fair cake-cutting」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.