TY - GEN

T1 - Analysis of a simple yet efficient convex hull algorithm

AU - Golin, Mordecai

AU - Sedgewick, Robert

N1 - Funding Information:
Convex hull algorithms can be seen as performing two separate tasks: The first is identifying those points actually on the hull, the second is eliminating those inside of it. Alternatively these 1This work supported in part by NSF Grant DCR-8605962 and Office of Naval Research Grant N00014-87-K-0460.

PY - 1988/1/6

Y1 - 1988/1/6

N2 - This paper is concerned with a simple, rather intuitive preprocessing step that is likely to improve the average-case performance of any convex hull algorithm. For n points randomly distributed in the unit square, we show that a simple linear pass through the points can eliminate all but O(√n) of the points by showing that a simple superset of the remaining points has size c√n + o(√n). We give a full implementation of the method, which should be useful in any practical application for finding convex hulls. Most of the paper is concerned with an analysis of the number of points eliminated by the procedure, including derivation of an exact expression for c. Extensions to higher dimensions are also considered.

AB - This paper is concerned with a simple, rather intuitive preprocessing step that is likely to improve the average-case performance of any convex hull algorithm. For n points randomly distributed in the unit square, we show that a simple linear pass through the points can eliminate all but O(√n) of the points by showing that a simple superset of the remaining points has size c√n + o(√n). We give a full implementation of the method, which should be useful in any practical application for finding convex hulls. Most of the paper is concerned with an analysis of the number of points eliminated by the procedure, including derivation of an exact expression for c. Extensions to higher dimensions are also considered.

UR - http://www.scopus.com/inward/record.url?scp=85013527084&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85013527084&partnerID=8YFLogxK

U2 - 10.1145/73393.73409

DO - 10.1145/73393.73409

M3 - Conference contribution

AN - SCOPUS:85013527084

T3 - Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988

SP - 153

EP - 163

BT - Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988

PB - Association for Computing Machinery, Inc

T2 - 4th Annual Symposium on Computational Geometry, SCG 1988

Y2 - 6 June 1988 through 8 June 1988

ER -