Search results for "Longest common substring problem"
showing 4 items of 4 documents
Linear-size suffix tries
2016
Suffix trees are highly regarded data structures for text indexing and string algorithms [MCreight 76, Weiner 73]. For any given string w of length n = | w | , a suffix tree for w takes O ( n ) nodes and links. It is often presented as a compacted version of a suffix trie for w, where the latter is the trie (or digital search tree) built on the suffixes of w. Here the compaction process replaces each maximal chain of unary nodes with a single arc. For this, the suffix tree requires that the labels of its arcs are substrings encoded as pointers to w (or equivalent information). On the contrary, the arcs of the suffix trie are labeled by single symbols but there can be Θ ( n 2 ) nodes and lin…
On the longest common factor problem
2008
The Longest Common Factor (LCF) of a set of strings is a well studied problem having a wide range of applications in Bioinformatics: from microarrays to DNA sequences analysis. This problem has been solved by Hui (2000) who uses a famous constant-time solution to the Lowest Common Ancestor (LCA) problem in trees coupled with use of suffix trees. A data structure for the LCA problem, although linear in space and construction time, introduces a multiplicative constant in both space and time that reduces the range of applications in many biological applications. In this article we present a new method for solving the LCF problem using the suffix tree structure with an auxiliary array that take…
On the construction of classes of suffix trees for square matrices: Algorithms and applications
1995
Given an n × n TEXT matrix with entries defined over an ordered alphabet σ, we introduce 4n−1 classes of index data structures for TEXT. Those indices are informally the two-dimensional analog of the suffix tree of a string [15], allowing on-line searches and statistics to be performed on TEXT. We provide one simple algorithm that efficiently builds any chosen index in those classes in O(n2 log n) worst case time using O(n2) space. The algorithm can be modified to require optimal O(n2) expected time for bounded σ.
On-line Construction of Two-Dimensional Suffix Trees
1999
AbstractWe say that a data structure is builton-lineif, at any instant, we have the data structure corresponding to the input we have seen up to that instant. For instance, consider the suffix tree of a stringx[1,n]. An algorithm building iton-lineis such that, when we have read the firstisymbols ofx[1,n], we have the suffix tree forx[1,i]. We present a new technique, which we refer to asimplicit updates, based on which we obtain: (a) an algorithm for theon-lineconstruction of the Lsuffix tree of ann×nmatrixA—this data structure is the two-dimensional analog of the suffix tree of a string; (b) simple algorithms implementing primitive operations forLZ1-typeon-line losslessimage compression m…