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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