Linear time algorithms for euclidean 1-center in Rd with non-linear convex constraints
Document Type
Conference Article
Publication Title
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
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 center of the minimum enclosing ball lies inside a given ball. We show that similar problem of minimum intersecting/ stabbing ball for set of hyper planes in Rd can also be solved using similar techniques. We also show how minimum intersecting disk with 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 complexity for fixed dimension.
First Page
126
Last Page
138
DOI
10.1007/978-3-319-29221-2_11
Publication Date
1-1-2016
Recommended Citation
Das, Sandip; Nandy, Ayan; and Sarvottamananda, Swami, "Linear time algorithms for euclidean 1-center in Rd with non-linear convex constraints" (2016). Conference Articles. 737.
https://digitalcommons.isical.ac.in/conf-articles/737
