Given an edge-weighted directed complete graph $G = (V,A)$, the maximum weight clique of fixed size $k$ ($k$ is a constant) can be identified in polynomial time with a brute-force algorithm, however the running time is impractical if $k$ is reasonably large.Is there a heuristic with provable approximation guarantees? Or any conditions on the weights that makes this problem easier?
Max weight k-clique
graph theory;graph algorithms;clique