r-indexing without backward searching: A New Approach to MEM-finding
Khái niệm cốt lõi
We introduce a new r-index approach for finding maximal exact matches (MEMs) without relying on backward searching, providing efficient and practical solutions.
Tóm tắt
Standalone Note:
Introduction
Knuth's conjecture on longest common substrings led to the development of suffix trees for MEM-finding.
Compressed suffix trees by Gagie, Navarro, and Prezza offer space-efficient alternatives.
Preliminaries
Lemma 1 explains the occurrence of substrings in T based on P's properties.
Corollary 2 simplifies the conditions for finding occurrences in T.
¯r-index
Utilizes LCS/LCP data structure and z-fast trie to efficiently index T for MEM-finding.
Corollary 2 guides the process of finding occurrences accurately with high probability.
Proof of Lemma 3
Ganardi, Je˙z, and Lohrey's method enables building an SLP for T with O(g) rules and height O(log n).
Recursive approach ensures efficient computation of LCS/P.
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r-indexing without backward searching
Thống kê
Let ¯r be the number of runs in the Burrows-Wheeler Transform of the reverse of T.