Linearized Suffix Tree: an Efficient Index Data Structure with the Capabilities of Suffix Trees and Suffix Arrays

Abstract

Suffix trees and suffix arrays are fundamental full-text index data structures to solve problems occurring in string processing. Since suffix trees and suffix arrays have different capabilities, some problems are solved more efficiently using suffix trees and others are solved more efficiently using suffix arrays. We consider efficient index data structures with the capabilities of both suffix trees and suffix arrays without requiring much space. When the size of an alphabet is small, enhanced suffix arrays are such index data structures. However, when the size of an alphabet is large, enhanced suffix arrays lose the power of suffix trees. Pattern searching in an enhanced suffix array takes O(m| |) time while pattern searching in a suffix tree takes O(m log | |) time where m is the length of a pattern and is an alphabet.In this paper, we present linearized suffix trees which are efficient index data structures with the capabilities of both suffix trees and suffix arrays even when the size of an alphabet is large. A linearized suffix tree has all the functionalities of the enhanced suffix array and supports the pattern search in O(m log | |) time. In a different point of view, it can be considered a practical implementation of the suffix tree supporting O(m log | |)-time pattern search.In addition, we also present two efficient algorithms for computing suffix links on the enhanced suffix array and the linearized suffix tree. These are the first algorithms that run in O(n) time without using the range minima query. Our experimental results show that our algorithms are faster than the previous algorithms.

Efficient multiple pattern matching algorithms for Network Intrusion Detection Systems

“…The linearized compact trie of P is an array representation of the compact trie of P, which provides branching for a character in O(log |A|) time and O(k) space [6]. This representation uses only simple arrays for branching information.…”

“…Second, on the LCP array, we define an lcp-interval [i, j] with length l such that sorted patterns from P i to P j share common prefix of length l. Formally, an lcp-interval with length l is an interval [6]. See Figure 5.…”

“…The DAWG or substring oracles are hard to implement, so this MBDM algorithm is not widely used in practice. Recently, new implementation of the DAWG including succinct DAWG [5] and linearized suffix trees [6] are proposed, so we try to apply the MBDM algorithms to NIDSs.…”

“…Then, we keep branching information of the lcpinterval tree in a table CLD of size k [6]. Therefore, a branching from [i, j] takes the time of logarithm of its number of children.…”

“…In this paper, we adapt a compact trie and its array representation, a linearized compact trie [6], to implement multiple pattern matching algorithms. In particular, we review Aho-Corasick and WuManber algorithms used in snort [11], and we propose efficient implementations of these algorithms based on linearized compact tries.…”