New PDF release: Algorithms and recursive functions

By A.I. Mal'cev

ISBN-10: 9001570704

ISBN-13: 9789001570705

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S prefix partitioning described above. Phoophakdee and Zaki [2007] proposed the Trellis partition-and-merge method. The DiGeST algorithm that performs essentially the multi-way merge-sort of suffixes was proposed by Barsky et al. [2008]. 43 CHAPTER 3 Scaling Up: When the Input Exceeds the Main Memory All the suffix tree construction algorithms described so far reduce random access to the suffix tree. Once the input string outgrows the main memory, these algorithms suffer severe performance degradation.

We partition X into two substrings X1 = abab with “tail” c and X2 = cababd. Note the overlapping symbol c that is used as a sentinel for suffixes of X1 . 10 (1), and output it to disk in the form of two different subtrees: one for prefix ab and the second for prefix ba. 10 (2)). Then, we load into main memory the subtrees for, say, prefix ab and we merge those sub-trees into the common ab-subtree for the entire X. The merge of subtrees for different chunks is performed by a straightforward character-bycharacter comparison, which leads to the same O(N 2 ) worst-case number of character comparisons as the brute force algorithms described before.

10 (1), and output it to disk in the form of two different subtrees: one for prefix ab and the second for prefix ba. 10 (2)). Then, we load into main memory the subtrees for, say, prefix ab and we merge those sub-trees into the common ab-subtree for the entire X. The merge of subtrees for different chunks is performed by a straightforward character-bycharacter comparison, which leads to the same O(N 2 ) worst-case number of character comparisons as the brute force algorithms described before. If we have k chunks and p prefixes in the variablelength prefixes collection, the number of random disk accesses is O(kp).

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Algorithms and recursive functions by A.I. Mal'cev


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