Detecting High Log-Densities -- an O(n^1/4) Approximation for Densest k-Subgraph

@inproceedings{Bhaskara2010DetectingHL,
title={Detecting High Log-Densities -- an O(n^1/4) Approximation for Densest k-Subgraph},
author={Aditya Bhaskara and Moses Charikar and Eden Chlamt{\'a}c and Uriel Feige and Aravindan Vijayaraghavan},
booktitle={STOC},
year={2010}
}

In the Densest k-Subgraph problem, given a graph G and a parameter k, one needs to find a subgraph of G induced on k vertices that contains the largest number of edges. There is a significant gap between the best known upper and lower bounds for this problem. It is NP-hard, and does not have a PTAS unless NP has subexponential time algorithms. On the other hand, the current best known algorithm of Feige, Kortsarz and Peleg, gives an approximation ratio of n1/3 - c for some fixed c>0 (later… CONTINUE READING