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The Computer Journal 1989 32(3):228-237; doi:10.1093/comjnl/32.3.228
© 1989 by British Computer Society
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An Approximation Algorithm for Space-optimal Encoding of a Text

J. Katajainen and T. Raita *

Department of Computer Science, University of Turku, SF-20520 Turku, Finland

In many situations text compression is carried out with a previously formed fixed dictionary (code book) expressing those often-occurring substrings of a text which are to be replaced by code words. The problem of encoding a text in a space-optimal manner is equivalent to the problem of finding a shortest path between a given pair of vertices in an acyclic and bandwidth-limited network. By combining an algorithm for finding shortest paths with the string matching algorithm of Aho and Corasick,1 a time-efficient approximation algorithm for the space-optimal encoding is obtained. The performance of the approximation algorithm depends on the amount of storage space available in the fast memory of a computer. With an unrestricted, though at most linear working storage on the length of the input text, a space-optimal encoding is obtained. However, even a fixed internal memory of moderate size guarantees almost optimal compression, and in spite of this the running time of the algorithm is comparable to that of the longest match heuristic.

Received April 1987.

* To whom corrrespondence should be addressed.

§ Department of Computer Science, University of Turku, SF-20520 Turku, Finland


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