Min-plus matrix multiplication

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Min-plus matrix multiplication, also known as distance product, is an operation on matrices.

Given two matrices and , their distance product is defined as an matrix such that . This is standard matrix multiplication for the semi-ring of tropical numbers in the min convention.

This operation is closely related to the shortest path problem. If is an matrix containing the edge weights of a graph, then gives the distances between vertices using paths of length at most edges, and is the distance matrix of the graph.


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