Shortest k-Cycle: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Shortest k-Cycle (Graph Cycles)}} == Description == Given a graph $G=(V,E)$ with non-negative weights, find a minimum weight cycle of length $k$. == Related Problems == Generalizations: Shortest Cycle == Parameters == <pre>n: number of vertices m: number of edges k: length of cycle</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reductions FROM Problem == {| class="wikitable sortable" sty...") |
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== Parameters == | == Parameters == | ||
$n$: number of vertices | |||
m: number of edges | |||
k: length of cycle | $m$: number of edges | ||
$k$: length of cycle | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Latest revision as of 09:28, 10 April 2023
Description
Given a graph $G=(V,E)$ with non-negative weights, find a minimum weight cycle of length $k$.
Related Problems
Generalizations: Shortest Cycle
Parameters
$n$: number of vertices
$m$: number of edges
$k$: length of cycle
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions FROM Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Min-Weight k-Clique | if: to-time: $O(nm^{\lceil k/{2} \rceil / \lambda - \epsilon})$ for any $\epsilon > {0}$ for $m = \Theta(n^{1+{1}/(\lambda - {1})}) edges and $n$ nodes where $\lambda = k - \lceil k/{2} \rceil + {1}$ then: from-time: $O(n^{k - \epsilon})$ for some $\epsilon > {0}$ |
2018 | https://arxiv.org/pdf/1712.08147v2.pdf, Corollary 4.2 | link |