Second Shortest Simple Path: Difference between revisions
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(Created page with "{{DISPLAYTITLE: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 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-sensiti...") |
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== Parameters == | == Parameters == | ||
$V$: number of vertices | |||
$E$: number of edges | |||
$L$: maximum absolute value of edge cost | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Latest revision as of 07:52, 10 April 2023
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.ezproxy.canberra.edu.au/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.ezproxy.canberra.edu.au/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.ezproxy.canberra.edu.au/doi/pdf/10.1145/3186893, Theorem 5.5 | link |