Skip to main content

Stochastic Closest-Pair Problem and Most-Likely Nearest-Neighbor Search in Tree Spaces

  • Conference paper
  • First Online:
Algorithms and Data Structures (WADS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10389))

Included in the following conference series:

Abstract

Let \(\mathcal {T}\) be a tree space represented by a weighted tree with t vertices, and S be a set of n stochastic points in \(\mathcal {T}\), each of which has a fixed location with an independent existence probability. We investigate two fundamental problems under such a stochastic setting, the closest-pair problem and the nearest-neighbor search. For the former, we propose the first algorithm of computing the \(\ell \)-threshold probability and the expectation of the closest-pair distance of a realization of S. For the latter, we study the k most-likely nearest-neighbor search (k-LNN) via a notion called the k most-likely Voronoi Diagram (k-LVD), where we show the combinatorial complexity of k-LVD is O(nk) under two reasonable assumptions, leading to a logarithmic query time for k-LNN.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Agarwal, P., Aronov, B., Har-Peled, S., Phillips, J., Yi, K., Zhang, W.: Nearest neighbor searching under uncertainty II. In: Proc. of the 32nd Sympos. on PODS, pp. 115–126. ACM (2013)

    Google Scholar 

  2. Agarwal, P., Cheng, S.W., Yi, K.: Range searching on uncertain data. ACM Transactions on Algorithms 8(4), 43 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Agarwal, P.K., Har-Peled, S., Suri, S., Yıldız, H., Zhang, W.: Convex hulls under uncertainty. In: Schulz, A.S., Wagner, D. (eds.) ESA 2014. LNCS, vol. 8737, pp. 37–48. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44777-2_4

    Google Scholar 

  4. Agarwal, P., Kumar, N., Sintos, S., Suri, S.: Range-max queries on uncertain data. In: Proc. of the 35th SIGMOD/PODS, pp. 465–476. ACM (2016)

    Google Scholar 

  5. Chen, J., Feng, L.: Efficient pruning algorithm for top-k ranking on dataset with value uncertainty. In: Proc. of the 22nd CIKM, pp. 2231–2236. ACM (2013)

    Google Scholar 

  6. Fakcharoenphol, J., Rao, S., Talwar, K.: Approximating metrics by tree metrics. ACM SIGACT News 35(2), 60–70 (2004)

    Article  MATH  Google Scholar 

  7. Fink, M., Hershberger, J., Kumar, N., Suri, S.: Hyperplane separability and convexity of probabilistic point sets. In: Proc. of the 32nd SoCG. ACM (2016)

    Google Scholar 

  8. Ge, T., Zdonik, S., Madden, S.: Top-\(k\) queries on uncertain data: on score distribution and typical answers. In: Proc. of the 2009 SIGMOD, pp. 375–388. ACM (2009)

    Google Scholar 

  9. Huang, L., Li, J.: Approximating the expected values for combinatorial optimization problems over stochastic points. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9134, pp. 910–921. Springer, Heidelberg (2015). doi:10.1007/978-3-662-47672-7_74

    Chapter  Google Scholar 

  10. Kamousi, P., Chan, T., Suri, S.: Stochastic minimum spanning trees in Euclidean spaces. In: Proc. of the 27th SoCG, pp. 65–74. ACM (2011)

    Google Scholar 

  11. Kamousi, P., Chan, T., Suri, S.: Closest pair and the post office problem for stochastic points. Computational Geometry 47(2), 214–223 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kumar, N., Raichel, B., Suri, S., Verbeek, K.: Most likely Voronoi Diagrams in higher dimensions. In: LIPIcs-Leibniz International Proceedings in Informatics, vol. 65. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2016)

    Google Scholar 

  13. Löffler, M., van Kreveld, M.: Largest and smallest convex hulls for imprecise points. Algorithmica 56(2), 235–269 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Suri, S., Verbeek, K.: On the most likely Voronoi Diagram and nearest neighbor searching. In: Ahn, H.-K., Shin, C.-S. (eds.) ISAAC 2014. LNCS, vol. 8889, pp. 338–350. Springer, Cham (2014). doi:10.1007/978-3-319-13075-0_27

    Google Scholar 

  15. Suri, S., Verbeek, K., Yıldız, H.: On the most likely convex hull of uncertain points. In: Bodlaender, H.L., Italiano, G.F. (eds.) ESA 2013. LNCS, vol. 8125, pp. 791–802. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40450-4_67

    Chapter  Google Scholar 

  16. Xue, J., Li, Y., Janardan, R.: On the separability of stochastic geometric objects, with applications. In: Proc. of the 32nd SoCG. ACM (2016)

    Google Scholar 

  17. Xue, J., Li, Y.: Stochastic closest-pair problem and most-likely nearest-neighbor search in tree spaces. arXiv:1612.04890 (2016)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yuan Li .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Xue, J., Li, Y. (2017). Stochastic Closest-Pair Problem and Most-Likely Nearest-Neighbor Search in Tree Spaces. In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-62127-2_48

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62126-5

  • Online ISBN: 978-3-319-62127-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics