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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 3-partition problem ： ウィキペディア英語版 3-partition problem The 3-partition problem is an NP-complete problem in computer science. The problem is to decide whether a given multiset of integers can be partitioned into triples that all have the same sum. More precisely, given a multiset ''S'' of ''n'' = 3 ''m'' positive integers, can ''S'' be partitioned into ''m'' triplets ''S''1, ''S''2, …, ''S''''m'' such that the sum of the numbers in each subset is equal? The subsets ''S''1, ''S''2, …, ''S''''m'' must form a partition of ''S'' in the sense that they are disjoint and they cover ''S''. Let ''B'' denote the (desired) sum of each subset ''S''''i'', or equivalently, let the total sum of the numbers in ''S'' be ''m'' ''B''. The 3-partition problem remains NP-complete when every integer in ''S'' is strictly between ''B''/4 and ''B''/2. In this case, each subset ''S''''i'' is forced to consist of exactly three elements (a triple). The 3-partition problem is similar to the partition problem, which in turn is related to the subset sum problem. In the partition problem, the goal is to partition ''S'' into two subsets with equal sum. In 3-partition the goal is to partition ''S'' into ''m'' subsets (or ''n''/3 subsets), not just two subsets, with equal sum. ==Strong NP-completeness== The 3-partition problem remains NP-complete even when the integers in ''S'' are bounded above by a polynomial in ''n''. In other words, the problem remains NP-complete even when representing the numbers in the input instance in unary. i.e., 3-partition is NP-complete in the strong sense or strongly NP-complete. This property, and 3-partition in general, is useful in many reductions where numbers are naturally represented in unary. In contrast, the partition problem is known to be NP-complete only when the numbers are encoded in binary, and have value exponential in ''n''. 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「3-partition problem」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.