Abstract
We study problems with stochastic uncertainty data on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration while minimizing the expected total query cost. We show that sorting in this scenario can be performed in polynomial time, while finding the data item with minimum value seems to be hard. This contradicts intuition, since the minimum problem is easier both in the online setting with adversarial inputs and in the offline verification setting. However, the stochastic assumption can be leveraged to beat both deterministic and randomized approximation lower bounds for the online setting. Although some literature has been devoted to minimizing query/probing costs when solving uncertainty problems with stochastic input, none of them have considered the setting we describe. Our approach is closer to the study of query-competitive algorithms, and it gives a better perspective on the impact of the stochastic assumption.
Partially supported by Icelandic Research Fund grant 174484-051 and by EPSRC grant EP/S033483/1. This work started while M.S.L. and T.T. were at Reykjavik University, during a research visit by S.C.
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Notes
- 1.
Note that, unless some sort of nondeterminism is allowed, the stochastic assumption cannot be used to improve the oblivious results, so we focus on adaptive algorithms.
References
Bruce, R., Hoffmann, M., Krizanc, D., Raman, R.: Efficient update strategies for geometric computing with uncertainty. Theory Comput. Syst. 38(4), 411–423 (2005). https://doi.org/10.1007/s00224-004-1180-4
Busto, D., Evans, W., Kirkpatrick, D.: Minimizing interference potential among moving entities. In: Proceedings of the 30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pp. 2400–2418 (2019). http://dl.acm.org/citation.cfm?id=3310435.3310582
Dürr, C., Erlebach, T., Megow, N., Meißner, J.: Scheduling with explorable uncertainty. In: Proceedings of the 9th Innovations in Theoretical Computer Science Conference, ITCS, LIPIcs, vol. 94, pp. 30:1–30:14 (2018). https://doi.org/10.4230/LIPIcs.ITCS.2018.30
Erlebach, T., Hoffmann, M.: Query-competitive algorithms for computing with uncertainty. Bull. EATCS 116, 22–39 (2015). http://bulletin.eatcs.org/index.php/beatcs/article/view/335
Erlebach, T., Hoffmann, M., Krizanc, D., Mihal’ák, M., Raman, R.: Computing minimum spanning trees with uncertainty. In: STACS, pp. 277–288 (2008). https://doi.org/10.4230/LIPIcs.STACS.2008.1358
Feder, T., Motwani, R., O’Callaghan, L., Olston, C., Panigrahy, R.: Computing shortest paths with uncertainty. J. Algorithms 62(1), 1–18 (2007). https://doi.org/10.1016/j.jalgor.2004.07.005
Goel, A., Guha, S., Munagala, K.: Asking the right questions: model-driven optimization using probes. In: Proceedings of the 25th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS, pp. 203–212 (2006). https://doi.org/10.1145/1142351.1142380
Goerigk, M., Gupta, M., Ide, J., Schöbel, A., Sen, S.: The robust knapsack problem with queries. Comput. Oper. Res. 55, 12–22 (2015). https://doi.org/10.1016/j.cor.2014.09.010
Gupta, A., Nagarajan, V.: A stochastic probing problem with applications. In: Goemans, M., Correa, J. (eds.) IPCO 2013. LNCS, vol. 7801, pp. 205–216. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36694-9_18
Gupta, A., Nagarajan, V., Singla, S.: Algorithms and adaptivity gaps for stochastic probing. In: Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete algorithms, SODA, pp. 1731–1747 (2016). https://doi.org/10.1137/1.9781611974331.ch120
Gupta, M., Sabharwal, Y., Sen, S.: The update complexity of selection and related problems. Theory Comput. Syst. 59(1), 112–132 (2016). https://doi.org/10.1007/s00224-015-9664-y
Halldórsson, M.M., de Lima, M.S.: Query-competitive sorting with uncertainty. In: Proceedings of the 44th International Symposium on Mathematical Foundations of Computer Science, MFCS, LIPIcs, vol. 138, pp. 7:1–7:15 (2019). https://doi.org/10.4230/LIPIcs.MFCS.2019.7
Kahan, S.: A model for data in motion. In: Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC, pp. 265–277 (1991). https://doi.org/10.1145/103418.103449
Megow, N., Meißner, J., Skutella, M.: Randomization helps computing a minimum spanning tree under uncertainty. SIAM J. Comput. 46(4), 1217–1240 (2017). https://doi.org/10.1137/16M1088375
Olston, C., Widom, J.: Offering a precision-performance tradeoff for aggregation queries over replicated data. In: Proceedings of the 26th International Conference on Very Large Data Bases, VLBD, pp. 144–155 (2000). http://ilpubs.stanford.edu:8090/437/
Ryzhov, I.O., Powell, W.B.: Information collection for linear programs with uncertain objective coefficients. SIAM J. Optim. 22(4), 1344–1368 (2012). https://doi.org/10.1137/12086279X
Singla, S.: The price of information in combinatorial optimization. In: Proceedings of the 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pp. 2523–2532 (2018). https://doi.org/10.1137/1.9781611975031.161
Welz, W.A.: Robot Tour Planning with High Determination Costs. Ph.D. thesis, Technischen Universität Berlin (2014). https://www.depositonce.tu-berlin.de/handle/11303/4597
Yamaguchi, Y., Maehara, T.: Stochastic packing integer programs with few queries. In: Proceedings of the 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pp. 293–310 (2018). https://dl.acm.org/doi/abs/10.5555/3174304.3175288
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Chaplick, S., Halldórsson, M.M., de Lima, M.S., Tonoyan, T. (2020). Query Minimization Under Stochastic Uncertainty. In: Kohayakawa, Y., Miyazawa, F.K. (eds) LATIN 2020: Theoretical Informatics. LATIN 2021. Lecture Notes in Computer Science(), vol 12118. Springer, Cham. https://doi.org/10.1007/978-3-030-61792-9_15
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