Structures Of String Matching And Data Compression by Jesper Larsson

By Jesper Larsson

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With natural languages, a reasonable word partitioning would consist of standard text delimiters: space, comma, carriage return, etc. We could also use implicit delimiters, as in the example in the preceding section. Using word suffix trees, large texts can be manipulated with a greatly reduced space requirement, as well as increased processing speed [9]. The table above indicates that the number of words, m, in common novels, is much less than the length of the work in bytes, n. This difference is even greater when one considers the number of distinct words, m .

Update p to point at the first bit after this symbol and go repeat from step 2. Assuming that b consecutive bits can be read in O(1) time, the time consumption for step 2 is constant. This step is performed a total number of O( N/b ) times. Case a of step 3 takes constant time plus the number of found word boundaries. Hence the total cost of this case is O(N/b + m). Case b of step 3 occurs when more than the last b/2 bits are occupied by a single symbol. It consumes time proportional to the number of bits in the symbol’s codeword each time it occurs.

Hence, maintaining the number of children requires memory corresponding to one symbol per internal node. Consequently, we can combine these observations with observation 1F to obtain the following conclusion: 2E Theorem A sliding window suffix tree indexing a window of maximum size M over an input of size n from an alphabet of size k can be maintained in expected O(n) time using storage for 5M + max {M, k} integers and 3M symbols. 32 Chapter Three Indexing Word-Partitioned Data T raditional suffix tree construction algorithms rely heavily on the fact that all suffixes are inserted, in order to obtain efficient time bounds.

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