Distance Product (Matrix Product)

Description

Matrix product over the $(\min, +)$-semiring

Related Problems

Related: Matrix Multiplication, Boolean Matrix Multiplication, Boolean Matrix Multiplication (Combinatorial), Matrix Product Verification, $(\min, \leq)$ Product

Parameters

n: dimension of square matrix

Table of Algorithms

Currently no algorithms in our database for the given problem.

Reductions TO Problem

Problem	Implication	Year	Citation	Reduction
Second Shortest Simple Path	if: to-time: $T(n,W)$ where there are $n$ nodes and integer weights in $({0}, W)$ then: from-time: $O(n^{2} T(O(n^{1/3}), O(nW)) \log W)$ for two $n\times n$ matrices with weights in $(-W, W)$	2018	https://dl.acm.org/doi/pdf/10.1145/3186893, Theorem 5.5	link

Reductions FROM Problem

Problem	Implication	Year	Citation	Reduction
Maximum Subarray	if: to-time: $O(n^{3-\epsilon})$ for some $\epsilon > {0}$ then: from-time: $O(n^{3-\epsilon})$	1998	https://dl.acm.org/doi/abs/10.5555/314613.314823	link