Composable core-sets for diversity and coverage maximization
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Composable core-sets.pdf
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Author(s)
Indyk, Piotr
Mahabadi, Sepideh
Mahdian, Mohammad
Mirrokni, Vahab S.
Date Issued
June 2014
Journal
Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '14
Publisher
Association for Computing Machinery
Citation
Indyk, Piotr, et al. "Composable Core-Sets for Diversity and Coverage Maximization." Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems - PODS '14, 22-27 June, 2014, New York, New York, ACM Press, 2014, pp. 100–08.
Version
Author's final manuscript
Abstract
In this paper we consider efficient construction of "composable core-sets" for basic diversity and coverage maximization problems. A core-set for a point-set in a metric space is a subset of the point-set with the property that an approximate solution to the whole point-set can be obtained given the core-set alone. A composable core-set has the property that for a collection of sets, the approximate solution to the union of the sets in the collection can be obtained given the union of the composable core-sets for the point sets in the collection. Using composable core-sets one can obtain efficient solutions to a wide variety of massive data processing applications, including nearest neighbor search, streaming algorithms and map-reduce computation.
Our main results are algorithms for constructing composable core-sets for several notions of "diversity objective functions", a topic that attracted a significant amount of research over the last few years. The composable core-sets we construct are small and accurate: their approximation factor almost matches that of the best "off-line" algorithms for the relevant optimization problems (up to a constant factor). Moreover, we also show applications of our results to diverse nearest neighbor search, streaming algorithms and map-reduce computation. Finally, we show that for an alternative notion of diversity maximization based on the maximum coverage problem small composable core-sets do not exist.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1145/2594538.2594560
