Composable Core-sets for Diversity and Coverage Maximization

  • Indyk P
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In this paper we consider ecient construction of \compos-able 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 approxi-mate 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 e-cient 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 com-posable core-sets for several notions of \diversity objective functions", a topic that attracted a signi cant 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 \o -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 alter-native notion of diversity maximization based on the max-imum coverage problem small composable core-sets do not exist.

Author-supplied keywords

  • core-set
  • diversity
  • map-
  • nearest neighbor
  • streaming

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  • Piotr Indyk

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