Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
A heuristic for the p-center problem in graphs
Discrete Applied Mathematics
An optimal-time algorithm for slope selection
SIAM Journal on Computing
Randomized optimal algorithm for slope selection
Information Processing Letters
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
More planar two-center algorithms
Computational Geometry: Theory and Applications
Optimal Parallel Algorithms for Problems Modeled by a Family of Intervals
IEEE Transactions on Parallel and Distributed Systems
Facility Location Constrained to a Polygonal Domain
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Efficient Algorithms for Two-Center Problems for a Convex Polygon
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Minimum-cost coverage of point sets by disks
Proceedings of the twenty-second annual symposium on Computational geometry
Line-segment intersection made in-place
Computational Geometry: Theory and Applications
Fast computation of smallest enclosing circle with center on a query line segment
Information Processing Letters
Constrained minimum enclosing circle with center on a query line segment
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
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Given a set P of n points and a straight line L, we study three important variations of minimum enclosing circle problem. The first problem is on computing k circles of minimum (common) radius with centers on L which can cover the members in P. We propose three algorithms for this problem. The first one runs in O(nk log n) time and O(n) space. The second one runs in O(nk+k2 log3 n) time and O(n log n) space assuming that the points are sorted along L, and is efficient where k ≪ n. The third one is based on parametric search and it runs in O(n log n + k log4 n) time. The next one is on computing the minimum radius circle centered on L that can enclose at least k points. The time and space complexities of the proposed algorithm are O(nk) and O(n) respectively. Finally, we study the situation where the points are associated with k colors, and the objective is to find a minimum radius circle with center on L such that at least one point of each color lies inside it. We propose an O(n log n) time algorithm for this problem.