Linear time algorithms for Euclidean 1-center in ℜd with non-linear convex constraints
Article Type
Research Article
Publication Title
Discrete Applied Mathematics
Abstract
In this paper, we first present a linear-time algorithm to find the smallest circle enclosing n given points in ℜ2 with the constraint that the center of the smallest enclosing circle lies inside a given disk. We extend this result to ℜ3 by computing constrained smallest enclosing sphere centered on a given sphere. We generalize the result for the case of points in ℜd where the center of the minimum enclosing ball lies inside a given ball. We show that similar problem of computing minimum intersecting/stabbing ball for a set of hyper planes in ℜd can also be solved using similar techniques. We also show how the minimum intersecting disk with the center constrained on a given disk can be computed to intersect a set of convex polygons. Lastly, we show that this technique is applicable when the center of minimum enclosing/intersecting ball lies in a convex region bounded by constant number of non-linear constraints with computability assumptions. We solve each of these problems in linear time in input size for fixed dimension.
DOI
10.1016/j.dam.2019.09.009
Publication Date
1-1-2019
Recommended Citation
Das, Sandip; Nandy, Ayan; and Sarvottamananda, Swami, "Linear time algorithms for Euclidean 1-center in ℜd with non-linear convex constraints" (2019). Journal Articles. 1009.
https://digitalcommons.isical.ac.in/journal-articles/1009