Max-Density Revisited: a Generalization and a More Efficient Algorithm

We present an algorithm that given a graph computes a subgraph of maximum ‘density’. (For unweighed graphs, density is the edges-to-vertices ratio). The proposed algorithm is asymptotically more efficient than the currently available ones. Our approach remains efficient for weighed graphs and more generally for weighed set-systems. Two faster approximation algorithms are offered, and a number of applications are discussed.