Abstract
Inspired by sports analysis, we study data structures for storing a trajectory representing the movement of a player during a game, such that the following queries can be answered: Given two positions s and t, report all sub-trajectories in which the player moved in a more or less straight line from s to t. We consider two measures of straightness, namely dilation and direction deviation, and present efficient construction algorithms for our data structures, and analyze their performance.
We also present an O(n1.5 + ε) algorithm that, given a trajectory P and a threshold τ, finds a simplification of P with a minimum number of vertices such that each edge in the simplification replaces a sub-trajectory of length at most τ times the length of the edge. This significantly improves the fastest known algorithm for the problem.
Research by MdB and AM was supported by the Netherlands Organization for Scientific Research (NWO) under projects 024.002.003 and 612.001.118, respectively.
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References
Agarwal, P.K., Matoušek, J., Sharir, M.: On range searching with semialgebraic sets II. SIAM J. Comput. 42, 2039–2062 (2013)
Agarwal, P.K., Klein, R., Knauer, C., Langerman, S., Morin, P., Sharir, M., Soss, M.A.: Computing the detour and spanning ratio of paths, trees, and cycles in 2D and 3D. Discr. Comput. Geom. 39, 17–37 (2008)
de. Berg, M., Cheong, O., van Kreveld, M., Overmars, M.: Computational Geometry: Algorithms and Applications, 3rd edn. Springer (2008)
de. Berg, M., Cook, A.F., Gudmundsson, J.: Fast Fréchet queries. Comput. Geom. Theory Appl. 46(6), 747–755 (2013)
Chazelle, B., Edelsbrunner, H., Guibas, L.J., Sharir, M.: A singly exponential stratification scheme for real semi-algebraic varieties and its applications. Theor. Comput. Sci. 84(1), 77–105 (1991)
Chazelle, B., Sharir, M., Welzl, E.: Quasi-optimal upper bounds for simplex range searching and new zone theorems. Algorithmica 8(5), 407–429 (1992)
Gudmundsson, J., Narasimhan, G., Smid, M.: Distance-preserving approximations of polygonal paths. Comput. Geom. Theory Appl. 36(3), 183–196 (2007)
Gudmundsson, J., Smid, M.: Fréchet queries in geometric trees. In: Bodlaender, H.L., Italiano, G.F. (eds.) ESA 2013. LNCS, vol. 8125, pp. 565–576. Springer, Heidelberg (2013)
Overmars, M. (ed.): The Design of Dynamic Data Structures. LNCS, vol. 156. Springer, Heidelberg (1983)
Pettersen, S.A., Johansen, D., Johansen, H., Berg-Johansen, V., Gaddam, V.R., Mortensen, A., Langseth, R., Griwodz, C., Stensland, H.K., Halvorsen, P.: Soccer video and player position dataset. In: Proc. 5th Int. Conf. Multi. Syst., pp. 18–23 (2014)
Shim, C.-B., Chang, J.-W., Kim, Y.-C.: Trajectory-based video retrieval for multimedia information systems. In: Yakhno, T. (ed.) ADVIS 2004. LNCS, vol. 3261, pp. 372–382. Springer, Heidelberg (2004)
Willard, D.E., Luecker, G.S.: Adding range restriction capability to dynamic data structures. J. ACM 32, 597–617 (1985)
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de Berg, M., Mehrabi, A.D. (2015). Straight-Path Queries in Trajectory Data. In: Rahman, M.S., Tomita, E. (eds) WALCOM: Algorithms and Computation. WALCOM 2015. Lecture Notes in Computer Science, vol 8973. Springer, Cham. https://doi.org/10.1007/978-3-319-15612-5_10
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DOI: https://doi.org/10.1007/978-3-319-15612-5_10
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