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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 Wiener connector ： ウィキペディア英語版 Wiener connector In mathematics applied to the study of networks, the Wiener connector, named in honor of chemist Harry Wiener who first introduced the Wiener Index, is a means of maximizing efficiency in connecting specified "query vertices" in a network. Given a connected, undirected graph and a set of query vertices in a graph, the minimum Wiener connector is a vertices-induced subgraph that connects the query vertices and minimizes the sum of shortest path distances among all pairs of vertices in the subgraph. In combinatorial optimization, the minimum Wiener connector problem is the problem of finding the minimum Wiener connector. It can be thought of as a version of the classic Steiner tree problem (one of Karp's 21 NP-complete problems), where instead of minimizing the size of the tree, the objective is to minimize the distances in the subgraph.〔(DIMACS Steiner Tree Challenge )〕 The minimum Wiener connector was first presented by Ruchansky, et. al. in 2015. The minimum Wiener connector has applications in many domains where there is a graph structure and an interest in learning about connections between sets of individuals. For example, given a set of patients infected with a viral disease, which other patients should be checked to find the culprit? Or given a set of proteins of interest, which other proteins participate in pathways with them? ==Problem definition== The Wiener index is the sum of shortest path distances in a (sub)graph. Using $d(u,v)$ to denote the shortest path between $u$ and $v$, the Wiener index of a (sub)graph $S$, denoted $W(S)$, is defined as : $W(S)\; =\; \backslash sum\_\; d(u,v)$. The minimum Wiener connector problem is defined as follows. Given an undirected and unweighted graph with vertex set $V$ and edge set $E$ and a set of query vertices $Q\backslash subseteq\; V$, find a connector $H\backslash subseteq\; V$ of minimum Wiener index. More formally, the problem is to compute : $\backslash operatorname$ *_H W(H\cup Q), that is, find a connector $H$ that minimizes the sum of shortest paths in $H$. 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「Wiener connector」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.