By Jesper Larsson
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Extra info for Structures Of String Matching And Data Compression
In the study of DNA sequences, we may represent a large variety of genetic substructures as words, from representations of single amino acids, up to entire gene sequences. In many such cases, the size of the overlying DNA string is substantially greater than the number of substructures it contains. As an example, there are merely tens of thousands of human genes, whilst the entire length of human DNA contains approximately three billion nucleotides. The word suffix tree is of particular importance in the case where the indexed string is not held in primary storage while the tree is utilized.
In addition, our algorithm requires less space than a suffix tree. Manber and Myers  presented an elegant radix-sorting based algorithm that takes at most O(n log n) time. They also suggested augmentations to allow string matching operations in time bounds close to those of the suffix tree, at the cost of additional space. Although our proposed algorithm is strongly related to that of Manber and Myers (it requires the same amount of space, has the same asymptotic worst case time complexity, and relies on the same suffix ordering observations), our algorithm gains a substantial advantage through reduction of superfluous processing.
Furthermore, steps 2, 4, and 6 take constant time and are performed once per recursive call, which is clearly less than n. Thus, the time for construction is O(n). 1 Assigning In-Order Numbers We perform an in-order traversal of the trie, and assign the leaves increasing numbers in the order they are visited, as shown in the figure on page 34. At each node, we take the order of the children to be the order in which they appear in the hash table. 2 3B Definition An assignment of numbers to strings is semi-lexicographic if and only if for all strings, α, β, and γ, where α and β have a common prefix that is not also a prefix of γ, the number assigned to γ is either less or greater than both numbers assigned to α and β.
Structures Of String Matching And Data Compression by Jesper Larsson