A test scheduling instance is specified by a set of elements, a set of tests, which are subsets of elements, and numeric priorities assigned to elements. The schedule is a sequence of test invocations with the goal of covering all elements. This formulation had been used to model problems in multiple application domains from network failure detection to broadcast scheduling. The modeling considered both SUM e and MAX e objectives, which correspond to average or worst-case cover times over elements (weighted by priority), and both one-time testing, where the goal is to detect if a fault is currently present, and continuous testing, performed in the background in order to detect presence of failures soon after they occur. Since all variants are NP hard, the focus is on approximations.

We present combinatorial approximations algorithms for both SUM e and MAX e objectives on continuous and MAX e on one-time schedules. The approximation ratios we obtain depend logarithmically on the number of elements and significantly improve over previous results. Moreover, our unified treatment of SUM e and MAX e objectives facilitates simultaneous approximation with respect to both.

Since one-time and continuous testing can be viable alternatives, we study their relation, which captures the overhead of continuous testing. We establish that for both SUM e and MAX e objectives, the ratio of the optimal one-time to continuous cover times is O(logn), where n is the number of elements. We show that this is tight as there are instances with ratio Ω(logn). We provide evidence, however, by considering Zipf distributions, that the typical ratio is lower.


Cover Time Deterministic Optimum Continuous Testing Broadcast Schedule Stochastic Schedule 
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  1. 1.
    Acharya, S., Alonso, R., Franklin, M., Zdonik, S.: Broadcast disks: data management for asymmetric communication environments. In: ACM SIGMOD (1995)Google Scholar
  2. 2.
    Ammar, M., Wong, J.: On the optimality of cyclic transmission in teletext systems. IEEE Tran. Communication 35(1), 68–73 (1987)CrossRefGoogle Scholar
  3. 3.
    Bar-Noy, A., Bhatia, R., Naor, J., Schieber, B.: Minimizing service and operation costs of periodic scheduling. Math. Oper. Res. 27(3), 518–544 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Bar-Noy, A., Dreizin, V., Patt-Shamir, B.: Efficient algorithms for periodic scheduling. Computer Networks 45(2), 155–173 (2004)zbMATHCrossRefGoogle Scholar
  5. 5.
    Cohen, E., Fiat, A., Kaplan, H.: Efficient sequences of trials. In: Proc. 14th ACM-SIAM Symposium on Discrete Algorithms (2003)Google Scholar
  6. 6.
    Cohen, E., Hassidim, A., Kaplan, H., Mansour, Y., Raz, D., Tzur, Y.: Probe scheduling for efficient detection of silent failures. Technical Report cs.NI/1302.0792, arXiv (2013)Google Scholar
  7. 7.
    Cohen, E., Shenker, S.: Replication strategies in unstructured peer-to-peer networks. In: Proceedings of the ACM SIGCOMM 2002 Conference (2002)Google Scholar
  8. 8.
    Feige, U.: A threshold of ln n for approximating set cover. J. Assoc. Comput. Mach. 45, 634–652 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Feige, U., Lovász, L., Tetali, P.: Approximating min-sum set cover. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) APPROX 2002. LNCS, vol. 2462, pp. 94–107. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Hameed, S., Vaidya, N.H.: Log-time algorithms for scheduling single and multiple channel data broadcast. In: Proc. of ACM/IEEE MobiCom (1997)Google Scholar
  11. 11.
    Kleinrock, L.: Queueing Systems. Computer Applications, vol. II. Wiley-Interscience, New York (1976)Google Scholar
  12. 12.
    Nguyen, H.X., Teixeira, R., Thiran, P., Diot, C.: Minimizing probing cost for detecting interface failures: Algorithms and scalability analysis. In: INFOCOM (2009)Google Scholar
  13. 13.
    Zeng, H., Kazemian, P., Varghese, G., McKeon, N.: Automatic test packet generation. In: CONEXT (2012)Google Scholar
  14. 14.
    Zheng, Q., Cao, G.: Minimizing probing cost and achieving identifiability in probe based network link monitoring. IEEE Tran. Computers 62(3), 510–523 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Edith Cohen
    • 1
    • 2
  • Haim Kaplan
    • 2
  • Yishay Mansour
    • 1
    • 3
  1. 1.Microsoft Research, SVCUSA
  2. 2.Tel Aviv UniversityIsrael
  3. 3.Microsoft ResearchIsrael

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