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

## 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

## 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 $(-W, W)$
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 $(-W, W)$
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 $(-W, W)$