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Covering a Set of Line Segments with a Few Squares

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Algorithms and Complexity (CIAC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12701))

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Abstract

We study three covering problems in the plane. Our original motivation for these problems come from trajectory analysis. The first is to decide whether a given set of line segments can be covered by up to four unit-sized, axis-parallel squares. The second is to build a data structure on a trajectory to efficiently answer whether any query subtrajectory is coverable by up to three unit-sized axis-parallel squares. The third problem is to compute a longest subtrajectory of a given trajectory that can be covered by up to two unit-sized axis-parallel squares.

The full version of this paper can be found at [7].

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References

  1. Agarwal, P.K., Procopiuc, C.M.: Exact and approximation algorithms for clustering. Algorithmica 33(2), 201–226 (2002)

    Article  MathSciNet  Google Scholar 

  2. Bereg, S., et al.: Optimizing squares covering a set of points. Theor. Comput. Sci. 729, 68–83 (2018)

    Article  MathSciNet  Google Scholar 

  3. Damiani, M.L., Issa, H., Cagnacci, F.: Extracting stay regions with uncertain boundaries from GPS trajectories: a case study in animal ecology. In: Proceedings of the 22nd ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pp. 253–262 (2014)

    Google Scholar 

  4. Drezner, Z.: On the rectangular \(p\)-center problem. Naval Res. Logistics (NRL) 34(2), 229–234 (1987)

    Article  MathSciNet  Google Scholar 

  5. Fowler, R.J., Paterson, M., Tanimoto, S.L.: Optimal packing and covering in the plane are NP-complete. Inf. Process. Lett. 12(3), 133–137 (1981)

    Article  MathSciNet  Google Scholar 

  6. Gudmundsson, J., Horton, M.: Spatio-temporal analysis of team sports. ACM Comput. Surv. (CSUR) 50(2), 22 (2017)

    Article  Google Scholar 

  7. Gudmundsson, J., van de Kerkhof, M., Renssen, A., Staals, F., Wiratma, L., Wong, S.: Covering a set of line segments with a few squares. CoRR, abs/2101.09913 (2021)

    Google Scholar 

  8. Gudmundsson, J., van Kreveld, M., Staals, F.: Algorithms for hotspot computation on trajectory data. In: Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pp. 134–143 (2013)

    Google Scholar 

  9. Hoffmann, M.: Covering polygons with few rectangles. In: Abstracts 17th European Workshop Computational Geometry, pp. 39–42 (2001)

    Google Scholar 

  10. Hwang, R.Z., Lee, R.C.T., Chang, R.C.: The slab dividing approach to solve the Euclidean \(p\)-center problem. Algorithmica 9(1), 1–22 (1993)

    Article  MathSciNet  Google Scholar 

  11. Megiddo, N., Supowit, K.J.: On the complexity of some common geometric location problems. SIAM J. Comput. 13(1), 182–196 (1984)

    Article  MathSciNet  Google Scholar 

  12. Nussbaum, D.: Rectilinear \(p\)-piercing problems. In: Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation, ISSAC, pp. 316–323 (1997)

    Google Scholar 

  13. Mahapatra, P.R.S., Goswami, P.P., Das, S.: Maximal covering by two isothetic unit squares. In: Canadian Conference on Computational Geometry, pp. 103–106 (2008)

    Google Scholar 

  14. Sadhu, S., Roy, S., Nandy, S.C., Roy, S.: Linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares. Theor. Comput. Sci. 769, 63–74 (2019)

    Article  MathSciNet  Google Scholar 

  15. Segal, M.: On piercing sets of axis-parallel rectangles and rings. Int. J. Comput. Geometry Appl. 9(3), 219–234 (1999)

    Article  MathSciNet  Google Scholar 

  16. Sharir, M., Agarwal, P.K.: Davenport-Schinzel Sequences and their Geometric Applications. Cambridge University Press, Cambridge (1995)

    MATH  Google Scholar 

  17. Sharir, M., Welzl, E.: Rectilinear and polygonal p-piercing and p-center problems. In: Proceedings of the 12th Annual Symposium on Computational Geometry, pp. 122–132 (1996)

    Google Scholar 

  18. Stohl, A.: Computation, accuracy and applications of trajectories–a review and bibliography. Dev. Environ. Sci. 1, 615–654 (2002)

    Google Scholar 

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Correspondence to Sampson Wong .

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Gudmundsson, J., van de Kerkhof, M., van Renssen, A., Staals, F., Wiratma, L., Wong, S. (2021). Covering a Set of Line Segments with a Few Squares. In: Calamoneri, T., Corò, F. (eds) Algorithms and Complexity. CIAC 2021. Lecture Notes in Computer Science(), vol 12701. Springer, Cham. https://doi.org/10.1007/978-3-030-75242-2_20

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  • DOI: https://doi.org/10.1007/978-3-030-75242-2_20

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