P. K. Agarwal and M. Sharir. Algorithmic techniques for geometric optimization. In Computer Science Today: Recent Trends and Developments, Lecture Notes in Computer Science, vol. 100 (J. van Leeuwen, ed.), Springer-Verlag, 1995. Home/Search Document Details and Download
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Mathematical Snapshots From the Computational Geometry Landscape - Matousek (Correct)
....log n, which would improve the range searching bound. For a more recent progress in range searching lower bounds, and some nice geometric problems, see [8] Many other areas and results would deserve to be mentioned, such as the developments related to linear programming algorithms (see the survey [1]) which also led to a nice purely mathematical application by Amenta [3] a short proof of a Helly type result) or the story of weak nets, born in computational geometry and later used by Alon and Kleitman [2] in their solution of the long open Hadwiger Debrunner problem in convex geometry, or ....
P. K. Agarwal and M. Sharir. Algorithmic techniques for geometric optimization. In Computer Science Today: Recent Trends and Developments, volume 1000 of Lecture Notes Comput. Sci., pages 234--253. Springer-Verlag, 1995.
Parametric and Kinetic Minimum Spanning Trees - Agarwal, Eppstein, Guibas.. (1998) (9 citations) Self-citation (Agarwal) (Correct)
....structures representing sets of edges in each cluster. We also apply several other techniques including parametric search (a technique of Megiddo [26] for turning decision algorithms into optimization algorithms, commonly used in both parametric optimization and computational geometry; see, e.g. [1]) and a data structure for maintaining convex hulls of a point set subject to insertions and undo operations. 1.1. Notation Throughout, we assume that we have a weighted, connected graph G = V, E) with n vertices and m edges, in which the weight of each edge e is a linear function w e (#) ....
P. K. Agarwal and M. Sharir. Algorithmic techniques for geometric optimization. In Computer Science Today: Recent Trends and Developments, Lecture Notes in Computer Science, vol. 100 (J. van Leeuwen, ed.), Springer-Verlag, 1995.
Rectilinear and Polygonal p-Piercing and p-Center Problems - Micha Sharir, Emo Welzl (1996) (23 citations) Self-citation (Sharir) (Correct)
....4 center problem can be solved in time O(n log n) which is worst case optimal, and the rectilinear 5 center problem can be solved in time O(n log 5 n) Remark. The Frederickson Johnson technique fails in the weighted case, where we need to apply full fledged parametric searching [29] see also [1, 2]) This results in O(n polylog n) solutions for both the weighted (or general) rectilinear 4 and 5 center problems. Details are given in the full version. 4 Polygonal 2 Piercing and 2Center Problems In this section we consider the 2 piercing and 2 center problems for convex polygons. In the ....
P.K. Agarwal and M. Sharir, Algorithmic techniques for geometric optimization, in: Lecture Notes in Computer Science, Vol. 1000, Springer-Verlag, 1995, pp. 234--253.
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