Convex optimization for the densest subgraph and densest submatrix problems

@article{Bombina2019ConvexOF,
title={Convex optimization for the densest subgraph and densest submatrix problems},
author={Polina Bombina and B. Ames},
journal={ArXiv},
year={2019},
volume={abs/1904.03272}
}

We consider the densest $k$-subgraph problem, which seeks to identify the $k$-node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We propose a new convex relaxation for the densest $k$-subgraph problem, based on a nuclear norm relaxation of a low-rank plus sparse decomposition of the adjacency matrices of $k$-node subgraphs to partially address this intractability. We establish that the densestâ€¦Â CONTINUE READING