On the minimum vocabulary problem

Abstract

The "minimum vocabulary problem" for a dictionary has applications in indexing and other domains of information retrieval. A simple directed-graph model of a dictionary results in a linear-time algorithm for this problem. Since it is known that many minimum vocabularies can exist for a dictionary, a computationally useful criterion for finding a "desirable minimum vocabulary" is suggested and an O(lV13) algorithm is outlined, where /VI is the number of words in the dictionary, duplicates eliminated. Furthermore, some enrichments to the model and the computational intractability of a variant called the l-lexicon problem are discussed. Directions for further work are indicated.