The Dynamic Dictionary Matching Problem Revisited

Abstract

The dynamic dictionary matching problem asks for a data structure to represent a set of pattern strings △={X1,X2,…,Xk},which can be updated efficiently when a pattern is inserted into or deleted form △, and which can support efficient searching of a text string to report all occurrences of the patterns of △. The work of Amir et al. [3,2] has produces an elegant solution supporting the update of △ for a pattern x in O(│x▕ log n ) time and the search of a text t in O((│t▕ + tocc)log n) time, where n denotes the total length of the patterns in △ and tocc denotes the total number of occurrences of the patterns in t. Recently, the time complexity of both operations has been improved, with the factor of log n replaced by log n/ log log n [4]. This paper presents a new solution in which an update takes O(│x▕ +log k) time and a search O((│t│ + tocc)log k) time. Moreover, we can further improve the search time to O((▕t│ + tocc) log k/log log k),but the update time increases to O(│x▕ log k / log log k).