The Asymmetric Matrix Partition Problem

Noga Alon, Michal Feldman, Iftah Gamzu, Moshe Tennenholtz

Abstract: An instance of the asymmetric matrix partition problem consists of a matrix \(A \in \mathbb{R}_+^{n \times m}\) and a probability distribution p over its columns. The goal is to find a partition scheme that maximizes the resulting partition value. A partition scheme \(\mathcal{S} = \{ \mathcal{S}_1, \ldots, \mathcal{S}_{n}\}\) consists of a partition \(\mathcal{S}_i\) of [m] for each row i of the matrix. The partition \(\mathcal{S}_i\) can be interpreted as a smoothing operator on row i, which replaces the value of each entry in that row with the expected value in the partition subset that contains it. Given a scheme \(\mathcal{S}\) that induces a smoothed matrix A′, the partition value is the expected maximum column entry of A′.

External IDs:dblp:conf/wine/AlonFGT13