Distance Product (Matrix Product)
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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 |