5,700 research outputs found
Near-optimal asymmetric binary matrix partitions
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 binary matrix and a
probability distribution over its columns. A partition scheme
consists of a partition for each row of . The partition acts
as a smoothing operator on row that distributes the expected value of each
partition subset proportionally to all its entries. Given a scheme that
induces a smooth matrix , the partition value is the expected maximum
column entry of . The objective is to find a partition scheme such that
the resulting partition value is maximized. We present a -approximation
algorithm for the case where the probability distribution is uniform and a
-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.Comment: 17 page
Near-optimal Asymmetric Binary Matrix Partitions
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 binary matrix and a probability distribution over its columns. A partition scheme consists of a partition for each row of . The partition acts as a smoothing operator on row that distributes the expected value of each partition subset proportionally to all its entries. Given a scheme that induces a smooth matrix , the partition value is the expected maximum column entry of . The objective is to find a partition scheme such that the resulting partition value is maximized. We present a -approximation algorithm for the case where the probability distribution is uniform and a -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
Near-Optimal Asymmetric Binary Matrix Partitions
We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al. (Proceedings of the 9th Conference on Web and Internet Economics (WINE), pp 1–14, 2013). Instances of the problem consist of an n× m binary matrix A and a probability distribution over its columns. A partition schemeB= (B1, … , Bn) consists of a partition Bifor each row i of A. The partition Biacts 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 AB, the partition value is the expected maximum column entry of AB. 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
Hashing for Similarity Search: A Survey
Similarity search (nearest neighbor search) is a problem of pursuing the data
items whose distances to a query item are the smallest from a large database.
Various methods have been developed to address this problem, and recently a lot
of efforts have been devoted to approximate search. In this paper, we present a
survey on one of the main solutions, hashing, which has been widely studied
since the pioneering work locality sensitive hashing. We divide the hashing
algorithms two main categories: locality sensitive hashing, which designs hash
functions without exploring the data distribution and learning to hash, which
learns hash functions according the data distribution, and review them from
various aspects, including hash function design and distance measure and search
scheme in the hash coding space
Optimized Cartesian -Means
Product quantization-based approaches are effective to encode
high-dimensional data points for approximate nearest neighbor search. The space
is decomposed into a Cartesian product of low-dimensional subspaces, each of
which generates a sub codebook. Data points are encoded as compact binary codes
using these sub codebooks, and the distance between two data points can be
approximated efficiently from their codes by the precomputed lookup tables.
Traditionally, to encode a subvector of a data point in a subspace, only one
sub codeword in the corresponding sub codebook is selected, which may impose
strict restrictions on the search accuracy. In this paper, we propose a novel
approach, named Optimized Cartesian -Means (OCKM), to better encode the data
points for more accurate approximate nearest neighbor search. In OCKM, multiple
sub codewords are used to encode the subvector of a data point in a subspace.
Each sub codeword stems from different sub codebooks in each subspace, which
are optimally generated with regards to the minimization of the distortion
errors. The high-dimensional data point is then encoded as the concatenation of
the indices of multiple sub codewords from all the subspaces. This can provide
more flexibility and lower distortion errors than traditional methods.
Experimental results on the standard real-life datasets demonstrate the
superiority over state-of-the-art approaches for approximate nearest neighbor
search.Comment: to appear in IEEE TKDE, accepted in Apr. 201
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