Sparse Suffix Tree Construction with Small Space
Philip Bille, Inge Li G{\o}rtz, Tsvi Kopelowitz, Benjamin, Sach, Hjalte Wedel Vildh{\o}j

TL;DR
This paper presents a new method for constructing sparse suffix trees efficiently in small space, with a time complexity of O(n log^2 b), and introduces a novel technique for space-efficient longest common prefix queries.
Contribution
The paper introduces a space-efficient construction algorithm for sparse suffix trees and a novel technique for fast LCP queries using minimal space.
Findings
Constructs sparse suffix trees in O(n log^2 b) time using O(b) space.
Develops a new technique for answering b LCP queries efficiently in small space.
Provides tradeoffs between space usage and construction time.
Abstract
We consider the problem of constructing a sparse suffix tree (or suffix array) for suffixes of a given text of size , using only words of space during construction time. Breaking the naive bound of time for this problem has occupied many algorithmic researchers since a different structure, the (evenly spaced) sparse suffix tree, was introduced by K{\"a}rkk{\"a}inen and Ukkonen in 1996. While in the evenly spaced sparse suffix tree the suffixes considered must be evenly spaced in , here there is no constraint on the locations of the suffixes. We show that the sparse suffix tree can be constructed in time. To achieve this we develop a technique, which may be of independent interest, that allows to efficiently answer longest common prefix queries on suffixes of , using only space. We expect that this technique will prove…
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Taxonomy
TopicsAlgorithms and Data Compression · DNA and Biological Computing · semigroups and automata theory
