Near-optimal asymmetric binary matrix partitions [article]

Fidaa Abed, Ioannis Caragiannis, Alexandros A. Voudouris
2015 arXiv   pre-print
We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al. (WINE 2013) to model the impact of asymmetric information on the revenue of the seller in take-it-or-leave-it sales. Instances of the problem consist of an n × m binary matrix A and a probability distribution over its columns. A partition scheme B=(B_1,...,B_n) consists of a partition B_i for each row i of A. The partition B_i acts as a smoothing operator on row i that distributes the expected
more » ... ue of each partition subset proportionally to all its entries. Given a scheme B that induces a smooth matrix A^B, the partition value is the expected maximum column entry of A^B. The objective is to find a partition scheme such that the resulting partition value is maximized. We present a 9/10-approximation algorithm for the case where the probability distribution is uniform and a (1-1/e)-approximation algorithm for non-uniform distributions, significantly improving results of Alon et al. Although our first algorithm is combinatorial (and very simple), the analysis is based on linear programming and duality arguments. In our second result we exploit a nice relation of the problem to submodular welfare maximization.
arXiv:1407.8170v3 fatcat:tr5jcdbmwvdcvhn7wyvxgxn7ri