Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Coping with Delays and Time-Outs in Binary Search Procedures

  • Conference paper
  • First Online:
Algorithms and Computation (ISAAC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1969))

Included in the following conference series:

Abstract

How many questions are necessary to guess an unknown number x in the set S = {1, 2,...,n}, by using only comparison questions, that is questions of the type “Is x ≤ a?”, when answers are received with a constant delay d; and up to a constant number c of the answers can be lost, i.e. can be not received at all? We exactly solve this problem for all integers d ≥ 0 and c = 1. We also briefly discuss the analogy between the above problem and that of broadcasting over a fully connected network with link latency.

This work was partially supported by an ENEA grant and by Progetto Cofinanziato: “Allocazioni di Risorse su Reti di Calcolatori”

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Aigner, Combinatorial Search, Wiley-Teubner, New York-Stuttgart, 1988.

    Google Scholar 

  2. M. Aigner, Searching with lies, J. Combinatorial Theory Ser. A, 74 (1995) 43–56.

    Article  MathSciNet  Google Scholar 

  3. S. Albers, M. Charikar, M. Mitzenmacher, Delayed Information and Action in On-line Algorithms, in Proc. of 39th FOCS, 1998, pp. 71–81.

    Google Scholar 

  4. A. Ambainis, S. A. Bloch, D. L. Schweizer, Delayed Binary Search, or Playing Twenty Questions with a Procrastinator, in Proc. of 10th AMC SIAM SODA (1999), pp. 844–845.

    Google Scholar 

  5. J. A. Aslam and A. Dhagat, Searching in the presence of linearly bounded errors, In: Proceedings of the 23rd ACM STOC (1991), pp. 486–493.

    Google Scholar 

  6. A. Bar-Noy, S. Kipnis, Designing Broadcast Algorithms in the Postal Model for Message-Passing Systems, Mathematical System Theory, vol 27 (1994), pp. 431–452.

    Article  MATH  MathSciNet  Google Scholar 

  7. D. Bertsekas, R. Gallager, Data Networks, 2nd edition, Perentice Hall (1992).

    Google Scholar 

  8. F. Cicalese, D. Mundici, Optimal binary search with two unreliable tests and minimum adaptiveness, In: Proc. European Symposium on Algorithms, ESA’ 99, J. Nesetril, Ed., Lecture Notes in Computer Science 1643 (1999), pp. 257–266.

    Google Scholar 

  9. F. Cicalese and U. Vaccaro, Optimal strategies against a liar, Theoretical Computer Science, 230 (1999), pp. 167–193.

    Article  MathSciNet  Google Scholar 

  10. A. Dhagat, P. Gacs, and P. Winkler, On Playing “Twenty Question” with a liar, In: Proc. 3rd ACM-SIAM SODA (1992), pp. 16–22.

    Google Scholar 

  11. M. Golin, A. Schuster, Optimal Point-to-Point Broadcast Algorithms via Lopsided Trees, Discrete Applied Mathematics, vol 93 (1999), pp. 233–263.

    Article  MATH  MathSciNet  Google Scholar 

  12. R. Hassin, M. Henig, Monotonicity and effcient computation of optimal dichotomous search, Discrete Applied Mathematics, 46 (1993), pp. 221–234.

    Article  MATH  MathSciNet  Google Scholar 

  13. K. Hinderer, M. Stieglitz, On polychotomous search problems, European Journal of Operational Research, 73 (1994), pp. 279–294.

    Article  MATH  Google Scholar 

  14. D. A. Huffman, A Method for the construction of Minimum Redundancy Codes, Proceedings of IRE, 40 (1952), pp. 1098–1101.

    Google Scholar 

  15. G. Katona, Combinatorial Search Problems, in: A Survey of Combinatorial Theory, North-Holland (1966), pp. 285–308.

    Google Scholar 

  16. D. Knuth, Searching and Sorting, The Art of Computer Programming, vol. 3, Massachusetts: Addison-Wesley (1998).

    Google Scholar 

  17. N. Linial, M. Sacks, Every Poset has a central Element, J. Combinatorial Theory A, 40 (1985), pp. 195–210.

    Article  MATH  Google Scholar 

  18. N. Linial, M. Sacks, Searching Ordered Structures, Journal of Algorithms, 6 (1985), pp. 86–103.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  20. A. Pelc, Detecting errors in searching games, J. Combinatorial Theory Ser. A, 51 (1989), pp. 43–54.

    Article  MATH  MathSciNet  Google Scholar 

  21. C. Picard, Theory of Questionnaires, Gauthier-Villars (1965), Paris.

    Google Scholar 

  22. R. L. Rivest, A. R. Meyer, D. J. Kleitman, K. Winklmann, J. Spencer, Coping with errors in binary search procedures, J. Computer and System Sciences, 20 (1980), pp. 396–404.

    Article  MATH  Google Scholar 

  23. J. Spencer, Ulam’s searching game with a fixed number of lies, Theoretical Computer Science, 95 (1992), pp. 307–321.

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, University of Salerno, 84081, Baronissi (SA), Italy

    Ferdinando Cicalese & Ugo Vaccaro

Authors
  1. Ferdinando Cicalese
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ugo Vaccaro
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Academia Sinica, Institute of Information Science, 128 Academia Road, Section 2, Nankang, 115, Taipei, Taiwan, R.O.C.

    D. T. Lee

  5. Department of Computer Science and Akamai Technologies, University of Illinois at Urbana Champaign, 500 Technology Square, 02139, Cambridge, MA, USA

    Shang-Hua Teng

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cicalese, F., Vaccaro, U. (2000). Coping with Delays and Time-Outs in Binary Search Procedures. In: Goos, G., Hartmanis, J., van Leeuwen, J., Lee, D.T., Teng, SH. (eds) Algorithms and Computation. ISAAC 2000. Lecture Notes in Computer Science, vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40996-3_9

Download citation

  • DOI: https://doi.org/10.1007/3-540-40996-3_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41255-7

  • Online ISBN: 978-3-540-40996-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation