Abstract
We address the problem of replicating a Voronoi diagram V(S) of a planar point set S by making proximity queries:
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the exact location of the nearest site(s) in S
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the distance to and label(s) of the nearest site(s) in S
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a unique label for every nearest site in S.
In addition to showing the limits of nearest-neighbor database security, our methods also provide one of the first natural algorithmic applications of retroactive data structures.
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References
Alevizos, P.D., Boissonnat, J.-D., Yvinec, M.: Non-convex contour reconstruction. J. Symbolic Comput. 10, 225–252 (1990)
Aoki, Y., Imai, H., Imai, K., Rappaport, D.: Probing a set of hyperplanes by lines and related problems. In: Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1993. LNCS, vol. 709, pp. 72–82. Springer, Heidelberg (1993)
Blelloch, G.E.: Space-efficient dynamic orthogonal point location, segment intersection, and range reporting. In: SODA 2008: Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 894–903. Society for Industrial and Applied Mathematics, Philadelphia (2008)
Boissonnat, J.-D., Yvinec, M.: Probing a scene of non-convex polyhedra. Algorithmica 8, 321–342 (1992)
Cheng, S.W., Janardan, R.: New results on dynamic planar point location. SIAM J. Comput. 21, 972–999 (1992)
Cole, R., Yap, C.K.: Shape from probing. J. Algorithms 8(1), 19–38 (1987)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications. Springer, Berlin (1997)
Demaine, E.D., Iacono, J., Langerman, S.: Retroactive data structures. ACM Trans. Algorithms 3(2), 13 (2007)
Dobkin, D.P., Edelsbrunner, H., Yap, C.K.: Probing convex polytopes. In: Proc. 18th Annu. ACM Sympos. Theory Comput., pp. 424–432 (1986)
Edelsbrunner, H., Skiena, S.S.: Probing convex polygons with x-rays. SIAM J. Comput. 17, 870–882 (1988)
Fortune, S.J.: A sweepline algorithm for Voronoi diagrams. Algorithmica 2, 153–174 (1987)
Giora, Y., Kaplan, H.: Optimal dynamic vertical ray shooting in rectilinear planar subdivisions. ACM Trans. Algorithms 5(3), 1–51 (2009)
Goodrich, M.T.: The mastermind attack on genomic data. In: IEEE Symposium on Security and Privacy. IEEE Press, Los Alamitos (2009) (to appear)
Joseph, E., Skiena, S.S.: Model-based probing strategies for convex polygons. Comput. Geom. Theory Appl. 2, 209–221 (1992)
McCreight, E.M.: Priority search trees. SIAM J. Comput. 14(2), 257–276 (1985)
Mehlhorn, K.: Data Structures and Algorithms 3: Multi-dimensional Searching and Computational Geometry. EATCS Monographs on Theoretical Computer Science, vol. 3. Springer, Heidelberg (1984)
Skiena, S.S.: Problems in geometric probing. Algorithmica 4, 599–605 (1989)
Skiena, S.S.: Probing convex polygons with half-planes. J. Algorithms 12, 359–374 (1991)
Skiena, S.S.: Interactive reconstruction via geometric probing. Proc. IEEE 80(9), 1364–1383 (1992)
Skiena, S.S.: Geometric reconstruction problems. In: Goodman, J.E., O’Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, ch. 26, pp. 481–490. CRC Press LLC, Boca Raton (1997)
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Dickerson, M.T., Eppstein, D., Goodrich, M.T. (2010). Cloning Voronoi Diagrams via Retroactive Data Structures. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_31
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DOI: https://doi.org/10.1007/978-3-642-15775-2_31
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