A New Compressed Suffix Tree Supporting Fast Search and Its Construction Algorithm Using Optimal Working Space

Abstract

The compressed suffix array and the compressed suffix tree for a given string S are full-text index data structures occupying O(nlog|Σ|) bits where n is the length of S and Σ is the alphabet from which symbols of S are drawn. When they were first introduced, they were constructed from suffix arrays and suffix trees, which implies they were not constructed in optimal O(nlog|Σ|)-bit working space. Recently, several methods were developed for constructing compressed suffix arrays and compressed suffix trees in optimal working space. By these methods, one can construct compressed suffix trees supporting the pattern search in O(m′ |Σ|) time where m′ = m logen, m is the length of a pattern, and logen is the time to find the ith smallest suffix of S from the compressed suffix array for any fixed 0 < e ≤ 1. However, compressed suffix trees supporting the pattern search in O(m′ log|Σ| ) time are not constructed by these methods. In this paper, we present a new compressed suffix tree supporting O(m′ log|Σ|)-time pattern search and its construction algorithm using optimal working space. To obtain this result, we developed a new succinct representation of the suffix trees, which is different from the classic succinct representation of parentheses encoding of the suffix trees. Our succinct representation technique can be generally applicable to succinct representation of other search trees.