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Theoretical and practical improvements on the RMQ-problem, with applications to LCA and LCE (2006)
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| Venue: | PROC. CPM. VOLUME 4009 OF LNCS |
| Citations: | 34 - 9 self |
BibTeX
@INPROCEEDINGS{Fischer06theoreticaland,
author = {Johannes Fischer and Volker Heun},
title = { Theoretical and practical improvements on the RMQ-problem, with applications to LCA and LCE},
booktitle = { PROC. CPM. VOLUME 4009 OF LNCS},
year = {2006},
pages = {36--48},
publisher = {Springer}
}
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Abstract
The Range-Minimum-Query-Problem is to preprocess an array such that the position of the minimum element between two specified indices can be obtained efficiently. We present a direct algorithm for the general RMQ-problem with linear preprocessing time and constant query time, without making use of any dynamic data structure. It consumes less than half of the space that is needed by the method by Berkman and Vishkin. We use our new algorithm for RMQ to improve on LCA-computation for binary trees, and further give a constant-time LCE-algorithm solely based on arrays. Both LCA and LCE have important applications, e.g., in computational biology. Experimental studies show that our new method is almost twice as fast in practice as previous approaches, and asymptotically slower variants of the constant-time algorithms perform even better for today’s common problem sizes.
Keyphrases
practical improvement general rmq-problem linear preprocessing time common problem size constant-time lce-algorithm constant query time specified index binary tree important application constant-time algorithm perform dynamic data structure new algorithm minimum element computational biology new method experimental study previous approach direct algorithm
