7,600 research outputs found
Worst-case efficient single and multiple string matching on packed texts in the word-RAM model
AbstractIn this paper, we explore worst-case solutions for the problems of single and multiple matching on strings in the word-RAM model with word length w. In the first problem, we have to build a data structure based on a pattern p of length m over an alphabet of size σ such that we can answer to the following query: given a text T of length n, where each character is encoded using logσ bits return the positions of all the occurrences of p in T (in the following we refer by occ to the number of reported occurrences). For the multi-pattern matching problem we have a set S of d patterns of total length m and a query on a text T consists in finding all positions of all occurrences in T of the patterns in S. As each character of the text is encoded using logσ bits and we can read w bits in constant time in the RAM model, we assume that we can read up to Θ(w/logσ) consecutive characters of the text in one time step. This implies that the fastest possible query time for both problems is O(nlogσw+occ). In this paper we present several different results for both problems which come close to that best possible query time. We first present two different linear space data structures for the first and second problem: the first one answers to single pattern matching queries in time O(n(1m+logσw)+occ) while the second one answers to multiple pattern matching queries to O(n(logd+logy+loglogmy+logσw)+occ) where y is the length of the shortest pattern. We then show how a simple application of the four Russian technique permits to get data structures with query times independent of the length of the shortest pattern (the length of the only pattern in case of single string matching) at the expense of using more space
Dynamic Relative Compression, Dynamic Partial Sums, and Substring Concatenation
Given a static reference string and a source string , a relative
compression of with respect to is an encoding of as a sequence of
references to substrings of . Relative compression schemes are a classic
model of compression and have recently proved very successful for compressing
highly-repetitive massive data sets such as genomes and web-data. We initiate
the study of relative compression in a dynamic setting where the compressed
source string is subject to edit operations. The goal is to maintain the
compressed representation compactly, while supporting edits and allowing
efficient random access to the (uncompressed) source string. We present new
data structures that achieve optimal time for updates and queries while using
space linear in the size of the optimal relative compression, for nearly all
combinations of parameters. We also present solutions for restricted and
extended sets of updates. To achieve these results, we revisit the dynamic
partial sums problem and the substring concatenation problem. We present new
optimal or near optimal bounds for these problems. Plugging in our new results
we also immediately obtain new bounds for the string indexing for patterns with
wildcards problem and the dynamic text and static pattern matching problem
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