TY - GEN

T1 - Expander-based-approach to geometric optimization

AU - Katz, Matthew J.

AU - Sharir, Micha

PY - 1993/1/1

Y1 - 1993/1/1

N2 - We present a new approach to problems in geometric optimization that are traditionally solved using the parametric searching technique of Megiddo. Our new approach is based on expander graphs and is conceptually much simpler and has more explicit geometric flavor. It does not require parallelization or randomization, and it exploits recent range-searching techniques of Matousek and others. We exemplify the technique on three problems, the slope selection problem, the planar distance selection problem, and the planar two-center problem. For the first problem we develop an O(n log3 n) solution, which, although suboptimal, is very simple. The second and third problems are more typical examples of our approach. Our solutions have, respectively, running time O(n4/3 log3+δ n), for any δ > 0, and O(n2 log3 n), comparable with the respective solutions of [2, 5].

AB - We present a new approach to problems in geometric optimization that are traditionally solved using the parametric searching technique of Megiddo. Our new approach is based on expander graphs and is conceptually much simpler and has more explicit geometric flavor. It does not require parallelization or randomization, and it exploits recent range-searching techniques of Matousek and others. We exemplify the technique on three problems, the slope selection problem, the planar distance selection problem, and the planar two-center problem. For the first problem we develop an O(n log3 n) solution, which, although suboptimal, is very simple. The second and third problems are more typical examples of our approach. Our solutions have, respectively, running time O(n4/3 log3+δ n), for any δ > 0, and O(n2 log3 n), comparable with the respective solutions of [2, 5].

UR - http://www.scopus.com/inward/record.url?scp=0027802768&partnerID=8YFLogxK

U2 - 10.1145/160985.161137

DO - 10.1145/160985.161137

M3 - Conference contribution

AN - SCOPUS:0027802768

SN - 0897915828

SN - 9780897915823

T3 - Proceedings of the 9th Annual Symposium on Computational Geometry

SP - 198

EP - 207

BT - Proceedings of the 9th Annual Symposium on Computational Geometry

PB - Publ by ACM

T2 - Proceedings of the 9th Annual Symposium on Computational Geometry

Y2 - 19 May 1993 through 21 May 1993

ER -