Abstract
We discuss two variations of the moving network Voronoi diagram. The first one addresses the following problem: given a network with n vertices and E edges. Suppose there are m sites (cars, postmen, etc) moving along the network edges and we know their moving trajectories with time information. Which site is the nearest one to a point p located on network edge at time t′? We present an algorithm to answer this query in O(log(mWlogm)) time with O(nmWlog2 m + n 2logn + nE) time and O(nmWlogm + E) space for preprocessing step, where E is the number of edges of the network graph (the definition of W is in section 3). The second variation views query point p as a customer with walking speed v. The question is which site he can catch the first? We can answer this query in O(m + log(mWlogm)) time with same preprocessing time and space as the first case. If the customer is located at some node, then the query can be answered in O(log(mWlogm)) time.
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References
Agarwal, K.P., Sharir, M.: Davenport–Schinzel Sequences and Their Geometric Applications. Cambridge University Press, Cambridge (1995)
Bae, S.W., Kim, J.-H., Chwa, K.-Y.: Optimal construction of the city voronoi diagram. In: ISAAC, pp. 183–192 (2006)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry Algorithms and Applications. Springer, Heidelberg (1997)
Devillers, O., Golin, M.J.: Dog bites postman: Point location in the moving voronoi diagram and related problems. In: Lengauer, T. (ed.) ESA 1993. LNCS, vol. 726, pp. 133–144. Springer, Heidelberg (1993)
Erwig, M.: The graph voronoi diagram with application. Networks 36, 156–163 (2000)
Guibas, L., Hershberger, J., Leven, D., Sharir, M., Tarjan, R.: Linear time algorithms for visibility and shortest path problems inside simple polygons. In: SCG 1986: Proceedings of the Second Annual Symposium on Computational Geometry, pp. 1–13. ACM, New York (1986)
Hakimi, S., Labbe, M., Schmeiche, E.: The voronoi partition of a network and its implications in location theory. INFIRMS Journal on Computing 4, 412–417 (1992)
Lee, D.T.: Two-dimensional voronoi diagrams in the lp-metric. Journal of the ACM 27(4), 604–618 (1980)
Okabe, A., Satoh, T., Furuta, T., Suzuki, A., Okano, K.: Generalized network voronoi diagrams: Concepts, computational methods, and applications. International Journal of Geographical Information Science 22(9), 965–994 (2008)
Ramalingam, G., Reps, T.: An incremental algorithm for a generalization of the shortest-path problem. Journal of Algorithms 21(2), 267–305 (1996)
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Fan, C., Luo, J. (2010). Point Location in the Continuous-Time Moving Network. In: Chen, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2010. Lecture Notes in Computer Science, vol 6124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14355-7_14
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DOI: https://doi.org/10.1007/978-3-642-14355-7_14
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