Affiliation:
1. University of Chile, Santiago, Chile
2. Brown University, Providence, RI
Abstract
The
intersection of sorted arrays
problem has applications in search engines such as Google. Previous work has proposed and compared deterministic algorithms for this problem, in an adaptive analysis based on the encoding size of a certificate of the result (cost analysis). We define the
alternation analysis
, based on the nondeterministic complexity of an instance. In this analysis we prove that there is a deterministic algorithm asymptotically performing as well as any randomized algorithm in the comparison model. We define the
redundancy analysis
, based on a measure of the internal redundancy of the instance. In this analysis we prove that any algorithm optimal in the redundancy analysis is optimal in the alternation analysis, but that there is a randomized algorithm which performs strictly better than any deterministic algorithm in the comparison model. Finally, we describe how these results can be extended beyond the comparison model.
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Cited by
14 articles.
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1. Optimizing RPQs over a compact graph representation;The VLDB Journal;2023-09-07
2. Document reordering for faster intersection;Proceedings of the VLDB Endowment;2019-01
3. Joins via Geometric Resolutions;ACM Transactions on Database Systems;2016-12-23
4. An efficient method to evaluate intersections on big data sets;Theoretical Computer Science;2016-09
5. Joins via Geometric Resolutions;Proceedings of the 34th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems;2015-05-20