Combinatorial Pair Testing: Distinguishing Workers from Slackers

  • David Eppstein
  • Michael T. Goodrich
  • Daniel S. Hirschberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)


We formalize a problem we call combinatorial pair testing (CPT), which has applications to the identification of uncooperative or unproductive participants in pair programming, massively distributed computing, and crowdsourcing environments. We give efficient adaptive and nonadaptive CPT algorithms and we show that our methods use an optimal number of testing rounds to within constant factors. We also provide an empirical evaluation of some of our methods.


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  1. 1.
    Atallah, M.J., Frikken, K.B., Blanton, M., Cho, Y.: Private combinatorial group testing. In: ACM Symp on Information, Computer and Communications Security (ASIACCS), pp. 312–320 (2008)Google Scholar
  2. 2.
    Beigel, R., Hurwood, W., Kahale, N.: Fault diagnosis in a flash. In: Proc. IEEE Foundations of Computer Science (FOCS), pp. 571–580 (October 1995)Google Scholar
  3. 3.
    Beigel, R., Kosaraju, S.R., Sullican, G.F.: Locating faults in a constant number of parallel testing rounds. In: ACM Symp. on Parallel Algorithms and Architectures (SPAA), pp. 189–198 (1989)Google Scholar
  4. 4.
    Beigel, R., Margulis, G., Spielman, D.A.: Fault diagnosis in a small constant number of parallel testing rounds. In: ACM Symp. on Parallel Algorithms and Architectures (SPAA), pp. 21–29 (1993)Google Scholar
  5. 5.
    Blecher, P.M.: On a logical problem. Discrete Mathematics 43(1), 107–110 (1983)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Du, D.-Z., Hwang, F.: Combinatorial Group Testing and Its Applications. Series on Applied Mathematics. World Scientific (2000)Google Scholar
  7. 7.
    Du, W., Goodrich, M.T.: Searching for high-value rare events with uncheatable grid computing. In: Ioannidis, J., Keromytis, A., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 122–137. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Du, W., Jia, J., Mangal, M., Murugesan, M.: Uncheatable grid computing. In: 24th Int. Conf. on Distributed Computing Systems (ICDCS), pp. 4–11 (2004)Google Scholar
  9. 9.
    Eppstein, D., Goodrich, M.T., Hirschberg, D.S.: Improved combinatorial group testing algorithms for real-world problem sizes. SIAM J. Comput. 36(5), 1360–1375 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Goodrich, M.T.: Pipelined algorithms to detect cheating in long-term grid computations. Theoretical Computer Science 408(2/3), 199–207 (2008)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Goodrich, M.T., Atallah, M.J., Tamassia, R.: Indexing information for data forensics. In: Ioannidis, J., Keromytis, A., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 206–221. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Hwang, F.K.: Random k-set pool designs with distinct columns. Probab. Eng. Inf. Sci. 14(1), 49–56 (2000)MATHCrossRefGoogle Scholar
  13. 13.
    Jacobson, N., Schaefer, S.K.: Pair programming in CS1: overcoming objections to its adoption. SIGCSE Bull. 40(2), 93–96 (2008)CrossRefGoogle Scholar
  14. 14.
    Liu, Q., Peng, J., Ihler, A.: Variational inference for crowdsourcing. In: Bartlett, P., Pereira, F.C.N., Burges, C.J.C., Bottou, L., Weinberger, K.Q. (eds.) Advances in Neural Information Processing Systems (NIPS), pp. 701–709 (2012)Google Scholar
  15. 15.
    Nagappan, N., Williams, L., Ferzli, M., Wiebe, E., Yang, K., Miller, C., Balik, S.: Improving the CS1 experience with pair programming. In: Proc. 34th SIGCSE Technical Symp. on Computer Science Education (SIGCSE 2003). SIGCSE Bulletin, vol. 35(1), pp. 359–362 (2003)Google Scholar
  16. 16.
    Niculescu, C.P., Vernescu, A.: A two-sided estimate of e x − (1 + x/n)n. Journal of Inequalities in Pure and Applied Mathematics 5(3) (2004)Google Scholar
  17. 17.
    Pelc, A., Upfal, E.: Reliable fault diagnosis with few tests. Comb. Probab. Comput. 7(3), 323–333 (1998)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Stadje, W.: The collector’s problem with group drawings. Advances in Applied Probability 22(4), 866–882 (1990)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Williams, L., Kessler, R.R.: Pair Programming Illuminated. Addison-Wesley (2003)Google Scholar
  20. 20.
    Williams, L., Kessler, R.R., Cunningham, W., Jeffries, R.: Strengthening the case for pair programming. IEEE Software 17(4), 19–25 (2000)CrossRefGoogle Scholar
  21. 21.
    Yao, A.C.: How to generate and exchange secrets. In: Proceedings of the 27th Annual Symposium on Foundations of Computer Science, pp. 162–167. IEEE Computer Society, Washington, DC (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • David Eppstein
    • 1
  • Michael T. Goodrich
    • 1
  • Daniel S. Hirschberg
    • 1
  1. 1.Dept. of Computer ScienceUniversity of CaliforniaIrvineUSA

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