Dagstuhl Report 13082: Communication Complexity, Linear Optimization, and lower bounds for the nonnegative rank of matrices

Communication Complexity, Linear Optimization, and lower bounds for the nonnegative rank of matrices (Dagstuhl Seminar 13082)

Lower bounds on nonnegative rank via nonnegative nuclear norms

The nonnegative rank of an entrywise nonnegative matrix A ∈ Rm×n + is the smallest integer r such that A can be written as A = UV where U ∈ Rm×r + and V ∈ Rr×n + are both nonnegative. The nonnegative rank arises in different areas such as combinatorial optimization and communication complexity. Computing this quantity is NP-hard in general and it is thus important to find efficient bounding tec...

Information-theoretic approximations of polytopes

Common information was introduced by Wyner [1975] as a measure of dependence of two random variables. This measure has been recently resurrected as a lower bound on the logarithm of the nonnegative rank of a nonnegative matrix in Jain et al. [2013], Braun and Pokutta [2013]. Lower bounds on nonnegative rank have important applications to several areas such as communication complexity and combin...

Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank

The nonnegative rank of a matrix A is the smallest integer r such that A can be written as the sum of r rank-one nonnegative matrices. The nonnegative rank has received a lot of attention recently due to its application in optimization, probability and communication complexity. In this paper we study a class of atomic rank functions defined on a convex cone which generalize several notions of “...

Complexity , Linear Optimization , and lower bounds for the nonnegative rank of matrices ( Dagstuhl Seminar 13082 )

This report documents the program and the outcomes of Dagstuhl Seminar 13061 “Fault Prediction, Localization, and Repair”. Software debugging, which involves localizing, understanding, and removing the cause of a failure, is a notoriously difficult, extremely time consuming, and human-intensive activity. For this reason, researchers have invested a great deal of effort in developing automated t...