Max-Weight k-Clique (Clique Problems)

From Algorithm Wiki
Jump to navigation Jump to search


Given a graph $G = (V, E)$, find the $k$-clique of maximum weight.

Related Problems

Generalizations: k-Clique

Related: Enumerating Maximal Cliques, arbitrary graph, Exact k-Clique, Min-Weight k-Clique


$n$: 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
Max-Weight Rectangle if: to-time: $O(N^{d-\epsilon})$ on $N$ weighted points in $d$ dimensions
then: from-time: $O(n^{k-\epsilon})$ on $n$ vertices, where $k=\lceil d^{2}\epsilon^{-1}\rceil$
2016 link
Maximum Subarray if: to-time: $O(n^{d+\lfloor d/{2}\rfloor-\epsilon})$ for $d$-dimensional hypercube arrays
then: from-time: $O(n^{k-\epsilon})$ on $n$ vertex graphs for $k=d+\lfloor d/{2}\rfloor$
2016 link