Convex optimization for the densest subgraph and densest submatrix problems

  title={Convex optimization for the densest subgraph and densest submatrix problems},
  author={Polina Bombina and B. Ames},
  • Polina Bombina, B. Ames
  • Published 2019
  • Mathematics, Computer Science
  • ArXiv
  • 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 densest… CONTINUE READING
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