Geometric Problems with Application to Hashing

Efficient algorithms are presented for two geometric problems. Both problems involve finding the best projection of a set of points from two-space onto a line, with two different notions of “best”. The key technique is to identify critical angles in between which the functions to be optimized have nice trigonometric forms that can be solved exactly. Applications to hashing arise when we look for the best linear combination of two hashing functions.

[1]  Renzo Sprugnoli,et al.  Perfect hashing functions , 1977, Commun. ACM.

[2]  Ronald L. Graham,et al.  An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..

[3]  Michael Ian Shamos,et al.  Geometric complexity , 1975, STOC.

[4]  Michael Ian Shamos,et al.  Closest-point problems , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[5]  F. P. Preparata,et al.  Convex hulls of finite sets of points in two and three dimensions , 1977, CACM.

[6]  Ray A. Jarvis,et al.  On the Identification of the Convex Hull of a Finite Set of Points in the Plane , 1973, Inf. Process. Lett..