On Atomic Cliques in Temporal Graphs

Atomic cliques were introduced recently to analyze comorbidity graphs that vary over time. We consider the atomic counterpart of the classical maximum clique problem in this paper. Our main contribution is a polynomial-time algorithm that transforms the maximum atomic clique problem to the maximum clique problem on an auxiliary graph. We report results from our … Read more

Robust convex relaxation for the planted clique and densest k-subgraph problems

We consider the problem of identifying the densest k-node subgraph in a given graph. We write this problem as an instance of rank-constrained cardinality minimization and then relax using the nuclear and l1 norms. Although the original combinatorial problem is NP-hard, we show that the densest k-subgraph can be recovered from the solution of our … Read more

Nuclear norm minimization for the planted clique and biclique problems

We consider the problems of finding a maximum clique in a graph and finding a maximum-edge biclique in a bipartite graph. Both problems are NP-hard. We write both problems as matrix-rank minimization and then relax them using the nuclear norm. This technique, which may be regarded as a generalization of compressive sensing, has recently been … Read more