Designing small keyboards is hard

Abstract

We study the problem of placing symbols of an alphabet onto the minimum number of keys on a small keyboard so that any word of a given dictionary can be recognized univoquely only by looking at the corresponding sequence of pressed keys. This problem is motivated by the design of small keyboards for mobile devices. We show that the problem is hard in general, and NP-complete even if we only wish to decide whether two keys are sufficient. We also consider two variants of the problem. In the first one, symbols on a same key must be contiguous in an ordered alphabet. The second variant is a fixed-parameter version of the previous one that minimizes a well-chosen measure of ambiguity in the recognition of the words for a given number of keys. Hardness and approximability results are given. © Springer-Verlag 2004.