Advertisement

Theory of Computing Systems

, Volume 59, Issue 1, pp 112–132 | Cite as

The Update Complexity of Selection and Related Problems

  • Manoj Gupta
  • Yogish Sabharwal
  • Sandeep SenEmail author
Article

Abstract

We present a framework for computing with input data specified by intervals, representing uncertainty in the values of the input parameters. To compute a solution, the algorithm can query the input parameters that yield more refined estimates in the form of sub-intervals and the objective is to minimize the number of queries. The previous approaches address the scenario where every query returns an exact value. Our framework is more general as it can deal with a wider variety of inputs and query responses and we establish interesting relationships between them that have not been investigated previously. Although some of the approaches of the previous restricted models can be adapted to the more general model, we require more sophisticated techniques for the analysis and we also obtain improved algorithms for the previous model. We address selection problems in the generalized model and show that there exist 2-update competitive algorithms that do not depend on the lengths or distribution of the sub-intervals and hold against the worst case adversary. We also obtain similar bounds on the competitive ratio for the MST problem in graphs.

Keywords

Query complexity Competitive ratio Interval data Models of uncertainty 

References

  1. 1.
    Aggarwal, C.C., Philip, S.Y.: A survey of uncertain data algorithms and applications. IEEE Trans. Knowl. Data Eng. 21(5), 609–623 (2009)CrossRefGoogle Scholar
  2. 2.
    Aron, I.D., Hentenryck, P.V.: On the complexity of the robust spanning tree problem with interval data. Oper. Res. Lett. 32(1), 36–40 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Beerliova, Z., Eberhard, F., Erlebach, T., Hall, A., Hoffmann, M., Mihalák, M., Shankar Ram, L.: Network discovery and verification. IEEE Journal on Selected Areas in Communications 24(12), 2168–2181 (2006)CrossRefGoogle Scholar
  4. 4.
    Bruce, R., Hoffmann, M., Krizanc, D., Raman, R.: Efficient update strategies for geometric computing with uncertainty. Theory Comput. Syst. 38(4), 411–423 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Feder, T., Motwani, R., O’Callaghan, L., Olston, C., Panigrahy, R.: Computing shortest paths with uncertainty. In: STACS, 367–378 (2003)Google Scholar
  6. 6.
    Feder, T., Motwani, R., Panigrahy, R., Olston, C., Widom, J.: Computing the median with uncertainty. SIAM J. Comput. 32(2), 538–547 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Goel, A., Guha, S., Munagala, K.: Asking the right questions: model-driven optimization using probes. In: PODS, 203–212 (2006)Google Scholar
  8. 8.
    Guha, S., Munagala, K.: Model-driven optimization using adaptive probes. In: SODA, 308–317 (2007)Google Scholar
  9. 9.
    Gupta, M., Sabharwal, Y., Sen, S.: The update complexity of selection and related problems. In: FSTTCS, 325–338 (2011)Google Scholar
  10. 10.
    Hoffmann, M., Erlebach, T., Krizanc, D., Mihalák, M., Raman, R.: Computing minimum spanning trees with uncertainty. In: STACS, 277–288 (2008)Google Scholar
  11. 11.
    Kahan, S.: A model for data in motion. In: STOC, 267–277 (1991)Google Scholar
  12. 12.
    Kasperski, A., Zielenski, P.: An approximation algorithm for interval data minmax regret combinatorial optimization problem. Inf. Process. Lett. 97(5), 177–180 (2006)CrossRefzbMATHGoogle Scholar
  13. 13.
    Khanna, S., Tan, W.C.: On computing functions with uncertainty. In: PODS, 171–182 (2001)Google Scholar
  14. 14.
    Olston, C., Widom, J.: Offering a precision-performance tradeoff for aggregation queries over replicated data. In: VLDB, 144–155 (2000)Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of CSEI.I.T. DelhiDelhiIndia
  2. 2.IBM Research - IndiaNew DelhiIndia

Personalised recommendations