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Searching for the Closest-Pair in a Query Translate

Authors Jie Xue, Yuan Li, Saladi Rahul, Ravi Janardan

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Author Details

Jie Xue
  • University of Minnesota, Twin Cities, Minneapolis, MN, USA
Yuan Li
  • Facebook Inc., Seattle, WA, USA
Saladi Rahul
  • University of Illinois at Urbana-Champaign, Urbana, IL, USA
Ravi Janardan
  • University of Minnesota, Twin Cities, Minneapolis, MN, USA

Funding

The research of Jie Xue is supported, in part, by a Doctoral Dissertation Fellowship from the Graduate School of the University of Minnesota.

Cite As Get BibTex

Jie Xue, Yuan Li, Saladi Rahul, and Ravi Janardan. Searching for the Closest-Pair in a Query Translate. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 61:1-61:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.SoCG.2019.61

Abstract

We consider a range-search variant of the closest-pair problem. Let Gamma be a fixed shape in the plane. We are interested in storing a given set of n points in the plane in some data structure such that for any specified translate of Gamma, the closest pair of points contained in the translate can be reported efficiently. We present results on this problem for two important settings: when Gamma is a polygon (possibly with holes) and when Gamma is a general convex body whose boundary is smooth. When Gamma is a polygon, we present a data structure using O(n) space and O(log n) query time, which is asymptotically optimal. When Gamma is a general convex body with a smooth boundary, we give a near-optimal data structure using O(n log n) space and O(log^2 n) query time. Our results settle some open questions posed by Xue et al. at SoCG 2018.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Closest pair
  • Range search
  • Geometric data structures
  • Translation query

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References

  1. M. A. Abam, P. Carmi, M. Farshi, and M. Smid. On the power of the semi-separated pair decomposition. In Workshop on Algorithms and Data Structures, pages 1-12. Springer, 2009. Google Scholar
  2. P. K. Agarwal, J. Pach, and M. Sharir. State of the union (of geometric objects): A review. Computational Geometry: Twenty Years Later. American Mathematical Society, 2007. Google Scholar
  3. Pankaj K Agarwal, Jeff Erickson, et al. Geometric range searching and its relatives. Contemporary Mathematics, 223:1-56, 1999. Google Scholar
  4. Sang Won Bae and Michiel Smid. Closest-Pair Queries in Fat Rectangles. arXiv preprint, 2018. URL: http://arxiv.org/abs/1809.10531.
  5. Herbert Edelsbrunner, Leonidas J Guibas, and Jorge Stolfi. Optimal point location in a monotone subdivision. SIAM Journal on Computing, 15(2):317-340, 1986. Google Scholar
  6. Prosenjit Gupta. Range-aggregate query problems involving geometric aggregation operations. Nordic Journal of Computing, 13(4):294-308, 2006. Google Scholar
  7. Prosenjit Gupta, Ravi Janardan, Yokesh Kumar, and Michiel Smid. Data structures for range-aggregate extent queries. Computational Geometry: Theory and Applications, 2(47):329-347, 2014. Google Scholar
  8. K. Kedem, R. Livne, J. Pach, and M. Sharir. On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles. Discrete &Computational Geometry, 1(1):59-71, 1986. Google Scholar
  9. N. Sarnak and R. E. Tarjan. Planar point location using persistent search trees. Communications of the ACM, 29(7):669-679, 1986. Google Scholar
  10. Jing Shan, Donghui Zhang, and Betty Salzberg. On spatial-range closest-pair query. In International Symposium on Spatial and Temporal Databases, pages 252-269. Springer, 2003. Google Scholar
  11. R. Sharathkumar and P. Gupta. Range-aggregate proximity queries. Technical Report IIIT/TR 80. IIIT Hyderabad, Telangana, 500032, 2007. Google Scholar
  12. Michiel Smid. Closest-point problems in computational geometry. In Handbook of computational geometry, pages 877-935. Elsevier, 2000. Google Scholar
  13. Jie Xue. Colored range closest-pair problem under general distance functions. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 373-390. SIAM, 2019. Google Scholar
  14. Jie Xue, Yuan Li, and Ravi Janardan. Approximate range closest-pair search. In Proceedings of the 30th Canadian Conference on Computational Geometry, pages 282-287, 2018. Google Scholar
  15. Jie Xue, Yuan Li, Saladi Rahul, and Ravi Janardan. New Bounds for Range Closest-Pair Problems. In Proceedings of the 34th International Symposium on Computational Geometry, pages 73:1-73:14, 2018. Google Scholar
  16. Jie Xue, Yuan Li, Saladi Rahul, and Ravi Janardan. Searching for the closest-pair in a query translate. arXiv preprint, 2018. URL: http://arxiv.org/abs/1807.09498.
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