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I/O-efficient planar range skyline and attrition priority queues

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Published:22 June 2013Publication History

ABSTRACT

We study the static and dynamic planar range skyline reporting problem in the external memory model with block size B, under a linear space budget. The problem asks for an O(n/B) space data structure that stores n points in the plane, and supports reporting the k maximal input points (a.k.a.skyline) among the points that lie within a given query rectangle Q = [α12] × [β1β2. When Q is 3-sided, i.e. one of its edges is grounded, two variants arise: top-open for β2 = ∞ and left-open for α1 = - ∞ (symmetrically bottom-open and right-open) queries.

We present optimal static data structures for top-open queries, for the cases where the universe is R2, a U × U grid, and rank space [O(n)]2. We also show that left-open queries are harder, as they require Ω((n/B)ε + k/B) I/Os for ε > 0, when only linear space is allowed. We show that the lower bound is tight, by a structure that supports 4-sided queries in matching complexities. Interestingly, these lower and upper bounds coincide with those of the planar orthogonal range reporting problem, i.e., the skyline requirement does not alter the problem difficulty at all!

Finally, we present the first dynamic linear space data structure that supports top-open queries in O(log2Bε n + k/B1 ε > and updates in O(log2Bε n) worst case I/Os, for ε ∈ [0, 1]. This also yields a linear space data structure for 4-sided queries with optimal query I/Os and O(log(n/B)) amortized update I/Os. We consider of independent interest the main component of our dynamic structures, a new real-time I/O-efficient and catenable variant of the fundamental structure priority queue with attrition by Sundar.

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        • Published in

          cover image ACM Conferences
          PODS '13: Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI symposium on Principles of database systems
          June 2013
          334 pages
          ISBN:9781450320665
          DOI:10.1145/2463664
          • General Chair:
          • Richard Hull,
          • Program Chair:
          • Wenfei Fan

          Copyright © 2013 ACM

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          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 22 June 2013

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          PODS '13 Paper Acceptance Rate24of97submissions,25%Overall Acceptance Rate476of1,835submissions,26%

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