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Heaps. Information Retrieval - Computational and Theoretical Aspects. Academic Press, 1978. J. Jensen, A. Spink, J. Bateman, and T. Saracevic. Real life information retrieval: A study of user queries on the Web. ACM SIGIR Forum, 32(1):5–17, 1998. W. Li. Random texts exhibit Zipf’s-law-like word frequency distribution. on Information Theory, 38(6): 1842–45, 1992. Udi Manber and Sun Wu. GLIMPSE: A tool to search through entire file systems. In Proc. of USENIX Technical Conference, pages 23–32, San Francisco, USA, January 1994.

In the case of small we have that the rank of the first word of length We also know that, since all the different words of length appear, they are uniformly distributed, and words of length are written, then the number of times each different word appears is which, under the light of Zipf’s law, shows that We consider the case of large now. As said, basically every typed word of this length is different, and therefore its frequency is 1. Since this must be we have where the last step considered that, as found before, the rank of this word is Equating the first and last term yields again Hence, the finite state model implies Zipf’s law, moreover, the value found is precisely where is the value for Heaps’ law.

Moreover, these indices are amenable to compression. Block-addressing indices can be reduced to 10% of their original size [Bell et al, 1993], and the first works on searching the text blocks directly in their compressed form are just appearing [Moura et al, 1998a; Moura et al, 1998] with very good performance in time and space. Resorting to sequential searching to solve a query may seem unrealistic for current Web search engine architectures, but makes perfect sense in a near future when a remote access could be as fast as a local access.

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50 Jahre Deutsche Statistische Gesellschaft Tagungen 1961 und 1962


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