Abstract
A dynamic algorithm can maintain the solution of a given problem under insertions and deletions of input objects. In this paper we propose a general scheme to obtain dynamic algorithms which is based on the abstract setting introduced by Clarkson and Shor. This scheme uses a novel data structure that combines the conflict graph and the history structure used by incremental algorithms. The randomized analysis of the dynamic algorithms assumes a probabilistic model of the update sequence, in which each currently present input object is equally likely to have been added by the previous insertion or to be deleted by the next deletion. We apply our general technique to obtain new and efficient algorithms for dynamically maintaining arrangements of line segments, lower envelopes of triangles, convex hulls and Voronoi diagrams of points in any dimension, and Voronoi diagrams of line segments in a plane.
This work has been partly supported by the ESPRIT Basic Research Action Program, under contract No. 7141 (project, ALCOM II).
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Dobrindt, K., Yvinec, M. (1993). Remembering conflicts in history yields dynamic algorithms. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_231
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DOI: https://doi.org/10.1007/3-540-57568-5_231
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