Nuclear norm minimization for the planted clique and biclique problems

Details Nuclear norm minimization for the planted clique and biclique problems Nuclear norm minimization for the planted clique and biclique problems

2009-01-21

arxiv.org/abs/0901.3348v1

Computer Science

Data Structures and Algorithms

Scientific paper

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 shown to be an effective way to solve rank optimization problems. In the special cases that the input graph has a planted clique or biclique (i.e., a single large clique or biclique plus diversionary edges), our algorithm successfully provides an exact solution to the original instance. For each problem, we provide two analyses of when our algorithm succeeds. In the first analysis, the diversionary edges are placed by an adversary. In the second, they are placed at random. In the case of random edges for the planted clique problem, we obtain the same bound as Alon, Krivelevich and Sudakov as well as Feige and Krauthgamer, but we use different techniques.

Affiliated with

Also associated with

No associations

Rating

Nuclear norm minimization for the planted clique and biclique problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nuclear norm minimization for the planted clique and biclique problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nuclear norm minimization for the planted clique and biclique problems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-188718