Composable core-sets for diversity and coverage maximization

• Main Authors: Indyk, Piotr (Contributor), Mahabadi, Sepideh (Contributor), Mahdian, Mohammad (Author), Mirrokni, Vahab S. (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
• Format: Article
• Language: English
• Published: Association for Computing Machinery, 2018-02-26T21:46:40Z.
• Subjects: Article
• Online Access: Get fulltext

 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.