Shortest Cycle: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Shortest Cycle (Graph Cycles)}} == Description == Given a graph $G=(V,E)$ with non-negative weights, find a minimum weight cycle. == Related Problems == Subproblem: Shortest k-Cycle == Parameters == <pre>n: number of vertices m: number of edges</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions FROM Problem == {| class="wikitable sortable" style="text-align:center;" width="100%"...") |
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== Parameters == | == Parameters == | ||
$n$: number of vertices | |||
m: number of edges | |||
$m$: number of edges | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Latest revision as of 08:28, 10 April 2023
Description
Given a graph $G=(V,E)$ with non-negative weights, find a minimum weight cycle.
Related Problems
Subproblem: Shortest k-Cycle
Parameters
$n$: number of vertices
$m$: number of edges
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions FROM Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Negative Triangle Detection | if: to-time: $T(n,M)$ where there are $n$ nodes and weights in $({1}, M)$ then: from-time: $T(n, O(M))$ where there are $n$ nodes and weights in $(-M, M)$ |
2018 | https://dl-acm-org.ezproxy.canberra.edu.au/doi/pdf/10.1145/3186893, Theorem 5.3 | link |