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Near-optimal Asymmetric Binary Matrix Partitions

Abed, F., Caragiannis, I., & Voudouris, A. A. (2014). Near-optimal Asymmetric Binary Matrix Partitions. Retrieved from http://arxiv.org/abs/1407.8170.

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Creators:
Abed, Fidaa1, Author
Caragiannis, Ioannis2, Author
Voudouris, Alexandros A.2, Author
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019
2External Organizations, ou_persistent22

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Free keywords: Computer Science, Computer Science and Game Theory, cs.GT,Computer Science, Computational Complexity, cs.CC
Abstract: 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 $n \times m$ 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 value 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.

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Language(s): eng - English
Dates: 2014-07-302014-07-30
Publication Status: Published online
Pages: 15 pages
Publishing info: -
Rev. Type: -
Identifiers: arXiv: 1407.8170
URI: http://arxiv.org/abs/1407.8170
BibTex Citekey: DBLP:journals/corr/AbedCV14
Degree: -

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