Chapter

Combinatorics, Algorithms, Probabilistic and Experimental Methodologies

Volume 4614 of the series Lecture Notes in Computer Science pp 459-470

A New Succinct Representation of RMQ-Information and Improvements in the Enhanced Suffix Array

  • Johannes FischerAffiliated withInst. für Informatik, Ludwig-Maximilians-Universität München, Amalienstr. 17, D-80333 München
  • , Volker HeunAffiliated withInst. für Informatik, Ludwig-Maximilians-Universität München, Amalienstr. 17, D-80333 München

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Abstract

The Range-Minimum-Query-Problem is to preprocess an array of length n in O(n) time such that all subsequent queries asking for the position of a minimal element between two specified indices can be obtained in constant time. This problem was first solved by Berkman and Vishkin [1], and Sadakane [2] gave the first succinct data structure that uses 4n + o(n) bits of additional space. In practice, this method has several drawbacks: it needs O(n logn) bits of intermediate space when constructing the data structure, and it builds on previous results on succinct data structures. We overcome these problems by giving the first algorithm that never uses more than 2n + o(n) bits, and does not rely on rank- and select-queries or other succinct data structures. We stress the importance of this result by simplifying and reducing the space consumption of the Enhanced Suffix Array [3], while retaining its capability of simulating top-down-traversals of the suffix tree, used, e.g., to locate all occ positions of a pattern p in a text in optimal O(|p| + occ) time (assuming constant alphabet size). We further prove a lower bound of 2n − o(n) bits, which makes our algorithm asymptotically optimal.