Search results for "Wavelet Tree"
showing 3 items of 3 documents
The Myriad Virtues of Wavelet Trees
2009
Wavelet Trees have been introduced in [Grossi, Gupta and Vitter, SODA '03] and have been rapidly recognized as a very flexible tool for the design of compressed full-text indexes and data compressors. Although several papers have investigated the beauty and usefulness of this data structure in the full-text indexing scenario, its impact on data compression has not been fully explored. In this paper we provide a complete theoretical analysis of a wide class of compression algorithms based on Wavelet Trees. We also show how to improve their asymptotic performance by introducing a novel framework, called Generalized Wavelet Trees, that aims for the best combination of binary compressors (like,…
On Table Arrangements, Scrabble Freaks, and Jumbled Pattern Matching
2010
Given a string s, the Parikh vector of s, denoted p(s), counts the multiplicity of each character in s. Searching for a match of Parikh vector q (a “jumbled string”) in the text s requires to find a substring t of s with p(t) = q. The corresponding decision problem is to verify whether at least one such match exists. So, for example for the alphabet Σ = {a, b, c}, the string s = abaccbabaaa has Parikh vector p(s) = (6,3,2), and the Parikh vector q = (2,1,1) appears once in s in position (1,4). Like its more precise counterpart, the renown Exact String Matching, Jumbled Pattern Matching has ubiquitous applications, e.g., string matching with a dyslectic word processor, table rearrangements, …
On Approximate Jumbled Pattern Matching in Strings
2011
Given a string s, the Parikh vector of s, denoted p(s), counts the multiplicity of each character in s. Searching for a match of a Parikh vector q in the text s requires finding a substring t of s with p(t) = q. This can be viewed as the task of finding a jumbled (permuted) version of a query pattern, hence the term Jumbled Pattern Matching. We present several algorithms for the approximate version of the problem: Given a string s and two Parikh vectors u, v (the query bounds), find all maximal occurrences in s of some Parikh vector q such that u <= q <= v. This definition encompasses several natural versions of approximate Parikh vector search. We present an algorithm solving this problem …