TY - GEN

T1 - Planar geometric location problems and maintaining the width of a planar set

AU - Agarwal, Pankaj K.

AU - Sharir, Micha

N1 - Publisher Copyright:
© 1991 Association for Computing Machinery. All rights reserved.

PY - 1991/3/1

Y1 - 1991/3/1

N2 - We present an O(n2 log3 n) algorithm for the two-center problem, in which we are given a set 5 of n points in the plane and wish to find two closed discs whose union contains S so that the larger of the two radii is as small as possible. We also give an O(n2 log5 n) algorithm for solving the two-line center problem, where we want to find two strips that cover S whose maximum width is as small as possible. To obtain the second result, we need as a subroutine an algorithm for determining whether the width of a given set S of points in the plane ever becomes less than or equal to a given parameter W > 0, as we perform n insertions and deletions on S, and the sequence of these operations is known in advance. We present an O(n log3 n) algorithm for solving this problem.

AB - We present an O(n2 log3 n) algorithm for the two-center problem, in which we are given a set 5 of n points in the plane and wish to find two closed discs whose union contains S so that the larger of the two radii is as small as possible. We also give an O(n2 log5 n) algorithm for solving the two-line center problem, where we want to find two strips that cover S whose maximum width is as small as possible. To obtain the second result, we need as a subroutine an algorithm for determining whether the width of a given set S of points in the plane ever becomes less than or equal to a given parameter W > 0, as we perform n insertions and deletions on S, and the sequence of these operations is known in advance. We present an O(n log3 n) algorithm for solving this problem.

UR - http://www.scopus.com/inward/record.url?scp=84921152398&partnerID=8YFLogxK

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AN - SCOPUS:84921152398

SN - 0897913760

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 449

EP - 458

BT - Proceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991

PB - Association for Computing Machinery

T2 - 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991

Y2 - 28 January 1991 through 30 January 1991

ER -