TY - JOUR

T1 - On some geometric selection and optimization problems via sorted matrices

AU - Glozman, Alex

AU - Kedem, Klara

AU - Shpitalnik, Gregory

N1 - Funding Information:
matrices. An m x n matrix M is a sorted matrix if each row and each column of M is in a nondecreasing order. Frederickson and Johnson have demonstrated that selection in a set of sorted matrices, that together represent the set 8, can be done in time sublinear in the size of 8. They have also observed that given certain constraints on the set 8, one can construct a set of sorted matrices representing 8. For instance, given two sorted arrays, X = {Xl ..... Xm} and Y = {Yl ..... Yn}, the Cartesian sum X + Y, defined as {xi + yj I 1 ~< i ~< m, 1 ~< j ~< n }, can be represented succinctly as a sorted matrix M by means of X A version of this paper appeared in Fourth Workshop on Algorithms and Data Structures, S.G. Akl, E Dehne, J. Sack and N. Santoro (Eds.), Lecture Notes in Computer Science 955, Springer-Verlag, pp. 26-35. * Corresponding author. E-mail: [email protected]. ! Work by K. Kedem has been supported by a grant from the U.S.-Israeli Binational Science Foundation, and by a grant from the Israel Science Foundation founded by The Israel Academy of Sciences and Humanities.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - In this paper we apply the selection and optimization technique of Frederickson and Johnson to a number of geometric selection and optimization problems, some of which have previously been solved by parametric search, and provide efficient and simple algorithms. Our technique improves the solutions obtained by parametric search by a log n factor. For example, we apply the technique to the two-line center problem, where we want to find two strips that cover a given set S of n points in the plane, so as to minimize the width of the largest of the two strips.

AB - In this paper we apply the selection and optimization technique of Frederickson and Johnson to a number of geometric selection and optimization problems, some of which have previously been solved by parametric search, and provide efficient and simple algorithms. Our technique improves the solutions obtained by parametric search by a log n factor. For example, we apply the technique to the two-line center problem, where we want to find two strips that cover a given set S of n points in the plane, so as to minimize the width of the largest of the two strips.

KW - Algorithm

KW - Computational geometry

KW - Optimization

KW - Selection

KW - Two-line center

UR - http://www.scopus.com/inward/record.url?scp=0040084561&partnerID=8YFLogxK

U2 - 10.1016/S0925-7721(98)00017-0

DO - 10.1016/S0925-7721(98)00017-0

M3 - Article

AN - SCOPUS:0040084561

SN - 0925-7721

VL - 11

SP - 17

EP - 28

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

IS - 1

ER -