Worst Case Efficient Single and Multiple String Matching in the RAM Model
نویسنده
چکیده
In 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 log σ 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 log σ bits and we can read w bits in constant time in the RAM model, we assume that we can read up to Θ(w/ log σ) consecutive characters of the text in one time step. This implies that the fastest possible query time for both problems is O(n log σ w +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 timeO(n( 1 m + log σ w )+occ) while the second one answers to multiple pattern matching queries to O(n( log d+log y+log logm y +
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