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The Update Complexity of Selection and Related Problems

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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.

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Notes

  1. So strictly speaking, the algorithm could take exponential time but may have a bounded competitive ratio.

  2. We can also handle semi-closed intervals but we have avoided further classification as they don’t lead to any interesting results.

  3. This was pointed out by an anonymous reviewer of a previous version.

References

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  5. Feder, T., Motwani, R., O’Callaghan, L., Olston, C., Panigrahy, R.: Computing shortest paths with uncertainty. In: STACS, 367–378 (2003)

  6. Feder, T., Motwani, R., Panigrahy, R., Olston, C., Widom, J.: Computing the median with uncertainty. SIAM J. Comput. 32(2), 538–547 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Goel, A., Guha, S., Munagala, K.: Asking the right questions: model-driven optimization using probes. In: PODS, 203–212 (2006)

  8. Guha, S., Munagala, K.: Model-driven optimization using adaptive probes. In: SODA, 308–317 (2007)

  9. Gupta, M., Sabharwal, Y., Sen, S.: The update complexity of selection and related problems. In: FSTTCS, 325–338 (2011)

  10. Hoffmann, M., Erlebach, T., Krizanc, D., Mihalák, M., Raman, R.: Computing minimum spanning trees with uncertainty. In: STACS, 277–288 (2008)

  11. Kahan, S.: A model for data in motion. In: STOC, 267–277 (1991)

  12. Kasperski, A., Zielenski, P.: An approximation algorithm for interval data minmax regret combinatorial optimization problem. Inf. Process. Lett. 97(5), 177–180 (2006)

    Article  MATH  Google Scholar 

  13. Khanna, S., Tan, W.C.: On computing functions with uncertainty. In: PODS, 171–182 (2001)

  14. Olston, C., Widom, J.: Offering a precision-performance tradeoff for aggregation queries over replicated data. In: VLDB, 144–155 (2000)

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Authors and Affiliations

  1. Department of CSE, I.I.T. Delhi, Delhi, India

    Manoj Gupta & Sandeep Sen

  2. IBM Research - India, New Delhi, India

    Yogish Sabharwal

Authors
  1. Manoj Gupta
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  2. Yogish Sabharwal
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  3. Sandeep Sen
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Correspondence to Sandeep Sen.

Additional information

A preliminary version of this paper appeared as [9]

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Gupta, M., Sabharwal, Y. & Sen, S. The Update Complexity of Selection and Related Problems. Theory Comput Syst 59, 112–132 (2016). https://doi.org/10.1007/s00224-015-9664-y

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  • DOI: https://doi.org/10.1007/s00224-015-9664-y

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