Min-plus matrix multiplication

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

, their distance product

matrix such that

min

{\displaystyle c_{ij}=\min _{k=1}^{n}\{a_{ik}+b_{kj}\}}

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.

matrix containing the edge weights of a graph, then

gives the distances between vertices using paths of length at most

is the distance matrix of the graph.

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