Min-Weight k-Clique: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Min-Weight k-Clique (Clique Problems)}} == Description == Given a graph $G = (V, E)$, find the $k$-clique of minimum weight. == Related Problems == Generalizations: k-Clique Related: Enumerating Maximal Cliques, arbitrary graph, Exact k-Clique, Max-Weight k-Clique == Parameters == <pre>n: number of vertices k: size of clique</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. == Reduct...") |
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== Parameters == | == Parameters == | ||
$n$: number of vertices | |||
k: size of clique | |||
$m$: number of edges | |||
$k$: size of clique | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Latest revision as of 09:22, 10 April 2023
Description
Given a graph $G = (V, E)$, find the $k$-clique of minimum weight.
Related Problems
Generalizations: k-Clique
Related: Enumerating Maximal Cliques, arbitrary graph, Exact k-Clique, Max-Weight k-Clique
Parameters
$n$: number of vertices
$m$: number of edges
$k$: size of clique
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions TO Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Minimum Weight k-Cycle | 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 |