# Second Shortest Simple Path (Shortest Path (Directed Graphs))

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## Description

Given a weighted digraph $G=(V,E)$, find the second shortest path between two given vertices $s$ and $t$.

## Related Problems

Generalizations: st-Shortest Path

Related: General Weights, Nonnegative Weights, Nonnegative Integer Weights, 1-sensitive (3/2)-approximate ss-shortest paths, 2-sensitive (7/5)-approximate st-shortest paths, 1-sensitive decremental st-shortest paths, 2-sensitive decremental st-shortest paths, Replacement Paths Problem

## Parameters

$V$: number of vertices

$E$: number of edges

$L$: maximum absolute value of edge cost

## Table of Algorithms

Currently no algorithms in our database for the given problem.

## Reductions FROM Problem

Problem | Implication | Year | Citation | Reduction |
---|---|---|---|---|

Minimum Triangle | if: to-time: $T(n,W)$ where there are $n$ nodes and integer weights in $({0}, W)$ then: from-time: $T(O(n), O(nW))$ for $n$ node graph with integer weights in $(-W, W)$ |
2018 | https://dl.acm.org/doi/pdf/10.1145/3186893, Theorem 5.5 | link |

Distance Product | 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 |

Directed, Weighted APSP | if: to-time: $T(n,W)$ where there are $n$ nodes and integer weights in $({0}, W)$ then: from-time: $O(n^{2} T(O(n^{1/3}), O(n^{2}W)) \log Wn)$ for graphs with weights in $(-W, W)$ |
2018 | https://dl.acm.org/doi/pdf/10.1145/3186893, Theorem 5.5 | link |