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Min-plus matrix multiplication : ウィキペディア英語版
Min-plus matrix multiplication
Min-plus matrix multiplication, also known as the distance product, is an operation on matrices.
Given two n \times n matrices A = (a_) and B = (b_), their distance product C = (c_) = A \star B is defined as an n \times n matrix such that c_ = \min_^n \\}.
This operation is closely related to the shortest path problem. If W is an n \times n matrix containing the edge weights of a graph, then W^k gives the distances between vertices using paths of length at most k edges, and W^n is the distance matrix of the graph.
== References ==

* Uri Zwick. 2002. (All pairs shortest paths using bridging sets and rectangular matrix multiplication ). ''J. ACM'' 49, 3 (May 2002), 289–317.
* Liam Roditty and Asaf Shapira. 2008. (All-Pairs Shortest Paths with a Sublinear Additive Error ). ICALP '08, Part I, LNCS 5125, pp. 622–633, 2008.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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