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Designing Small Keyboards Is Hard

  • Jean Cardinal
  • Stefan Langerman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)

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.

Keywords

Mobile Phone Word Pair Ambiguous Word Submodular Function Text Entry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    ISO/IEC 9995-8. Information systems – keyboard layouts for text and office systems – part 8: Allocation of letters to keys of a numeric keypad (1994), International Organisation for standardisation Google Scholar
  2. 2.
    Bellare, M., Goldreich, M., Sudan, M.: Free bits, PCPs and non-approximability – towards tight results. SIAM J. Comp. 27, 804–915 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Butts, L., Cockburn, A.: An evaluation of mobile phone text input methods. In: Proc. 3rd Australasian User Interfaces Conference (2001)Google Scholar
  4. 4.
    Tegic Communications. T9 text entry, http://www.t9.com
  5. 5.
    Conforti, M., Cornuejols, G.: Submodular functions, matroids and the greedy algorithm: tight worst-case bounds and some generalizations of the Rado-Edmonds theorem. Discrete Applied Mathematics 7, 257–275 (1984)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Garey, M., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)zbMATHGoogle Scholar
  7. 7.
    Hochbaum, D.S. (ed.): Approximation algorithms for NP-hard problems. PWS Publishing Company (1997)Google Scholar
  8. 8.
    Lesher, G., Moulton, B., Jeffery Higginbotham, D.: Optimal character arrangements for ambiguous keyboards. IEEE Trans. on Rehabilitation Engineering 6(4) (1998)Google Scholar
  9. 9.
    MacKenzie, I., Soukoreff, R.: Text entry for mobile computing: Models and methods, theory and practice. Human-Computer Interaction 17, 147–198 (2002)CrossRefGoogle Scholar
  10. 10.
    Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and a subconstant error-probability PCP characterization of NP. In: Proceedings of the 29th ACM Symposium on Theory of Computing, pp. 475–484 (1997)Google Scholar
  11. 11.
    Vazirani, V.: Approximation Algorithms. Springer, Berlin (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jean Cardinal
    • 1
  • Stefan Langerman
    • 1
  1. 1.Computer Science DepartmentUniversité Libre de BruxellesBrusselsBelgium

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