Optimal Succinctness for Range Minimum Queries
Abstract
For a static array A of n ordered objects, a range minimum query asks for the position of the minimum between two specified array indices. We show how to preprocess A into a scheme of size 2n+o(n) bits that allows to answer range minimum queries on A in constant time. This space is asymptotically optimal in the important setting where access to A is not permitted after the preprocessing step. Our scheme can be computed in linear time, using only n + o(n) additional bits at construction time. In interesting by-product is that we also improve on LCA-computation in BPS- or DFUDS-encoded trees.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2008
- DOI:
- 10.48550/arXiv.0812.2775
- arXiv:
- arXiv:0812.2775
- Bibcode:
- 2008arXiv0812.2775F
- Keywords:
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- Computer Science - Data Structures and Algorithms;
- E.1
- E-Print:
- 12 pages