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Quasi-Perfect Minimally Adaptive q-ary Search with Unreliable Tests

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Algorithms and Computation (ISAAC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2906))

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Abstract

We consider the problem of determining the minimum number of queries to find an unknown number in a finite set when up to a finite number e of the answers may be erroneous. In the vast literature regarding this problem, the classical case of binary search is mostly considered, that is, when only yes-no questions are allowed. In this paper we consider the variant of the problem in which questions with q many possible answers are allowed. We prove that at most one question more than the information theoretic lower bound is sufficient to successfully find the unknown number. Moreover we prove that there are infinitely many cases when the information theoretic lower bound is exactly attained and the so called perfect strategies exist. Our strategies have the important feature that they use a minimum amount of adaptiveness, a relevant property in many practical situation.

This work was partially supported by INTAS 00-738

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References

  1. Aigner, M.: Searching with lies. J. Comb. Theory, Ser. A 74, 43–56 (1995)

    Article  MathSciNet  Google Scholar 

  2. Berlekamp, E.R.: Block coding for the binary symmetric channel with noiseless, delayless feedback. In: Mann, H.B. (ed.) Error-correcting Codes, pp. 61–88. Wiley, New York (1968)

    Google Scholar 

  3. Cicalese, F., Vaccaro, U.: Optimal strategies against a liar. Theoretical Computer Science 230, 167–193 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cicalese, F., Mundici, D., Vaccaro, U.: Least adaptive optimal search with unreliable tests. Theoretical Computer Science 270(1-2), 877–893 (2001)

    Article  MathSciNet  Google Scholar 

  5. Czyzowicz, J., Mundici, D., Pelc, A.: Ulam’s searching game with lies. J. Comb. Theo., Ser. A 52, 62–76 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  6. Deppe, C.: Solution of Ulam’s searching game with three lies or an optimal adaptive strategy for binary three-error-correcting codes. Discrete Math. 224(1-3), 79–98 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Guzicki, W.: Ulam’s Searching Game with Two Lies. J. Combin. Theory Ser. A 54, 1–19 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  8. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1977)

    MATH  Google Scholar 

  9. Malinowski: K-ary searching with a lie. Ars Combinatoria 37, 301–308 (1994)

    MATH  MathSciNet  Google Scholar 

  10. Muthukrishnan, S.: On optimal strategies for searching in presence of errors. In: Proc. of the 5th ACM-SIAM SODA, pp. 680–689 (1994)

    Google Scholar 

  11. Negro, A., Sereno, M.: Ulam’s searching game with three lies. Adv. in Appl. Math. 13, 404–428 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  12. Pelc, A.: Solution of Ulam’s problem on searching with a lie. J. Combin. Theory, Ser. A 44, 129–142 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  13. Pelc, A.: Search games with errors – Fifty years of coping with liars (2000) (preprint)

    Google Scholar 

  14. Rényi, A.: Napló az információelméletről, Gondolat, Budapest (1976); (English translation: A Diary on Information Theory, J.Wiley and Sons, New York, 1984)

    Google Scholar 

  15. Spencer, J.: Ulam’s searching game with a fixed number of lies. Theoretical Comp. Sci. 95, 307–321 (1992)

    Article  MATH  Google Scholar 

  16. Tietäväinen, A.: On the nonexistence of perfect codes over finite fields. SIAM J. Appl. Math. 24, 88–96 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  17. Ulam, S.M.: Adventures of a Mathematician, Scribner’s, New York (1976)

    Google Scholar 

  18. Zinoviev, V.A., Leontiev, V.K.: The non-existence of perfect codes over Galois fields. Probl. Contr. Inform. Theory 2, 123–132 (1973)

    Google Scholar 

  19. Zinoviev, V.A., Katsman, G.L.: Universal Code Families. Information Theory and Coding Theory 29(2), 95–100 (1993)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science and Appl., Univ. of Salerno, 84081, Baronissi, (SA), Italy

    Ferdinando Cicalese

  2. Dept. of Mathematics, Univ. of Bielefeld, D-33501, Bielefeld, Germany

    Christian Deppe

Authors
  1. Ferdinando Cicalese
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  2. Christian Deppe
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Editor information

Editors and Affiliations

  1. School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

    Toshihide Ibaraki

  2. Department of Architecture and Architectural Engineering, Kyoto University, 615-8540, Nishikyo-ku, Kyoto, Japan

    Naoki Katoh

  3. Department of Computer Science and Communication Engineering, Kyushu University, 812-8581, Fukuoka, Japan

    Hirotaka Ono

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© 2003 Springer-Verlag Berlin Heidelberg

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Cicalese, F., Deppe, C. (2003). Quasi-Perfect Minimally Adaptive q-ary Search with Unreliable Tests . In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_54

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  • DOI: https://doi.org/10.1007/978-3-540-24587-2_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20695-8

  • Online ISBN: 978-3-540-24587-2

  • eBook Packages: Springer Book Archive

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