TY - JOUR

T1 - A New Point-Location Algorithm and its Practical Efficiency—Comparison with Existing Algorithms

AU - Edahiro, Masato

AU - Kokubo, Iwao

AU - Asano, Takao

PY - 1984/4/1

Y1 - 1984/4/1

N2 - The point-location problem is stated as follows: Given a subdivision of the plane by a straight line planer graph G with n vertices and an arbitrary query point Q, determine which region of the subdivision contains Q. A new practical point-location algorithm is proposed. It has 0(1) search time, O(n) space, and O(n) preprocessing time in the average case. Existing point-location algorithms, as well as the one proposed here, have been implemented in FORTRAN, and their practical efficiencies are investigated by computational experiments on several planar subdivisions defined by graphs with 200-4000 vertices. It is shown that our 0(1) search-time, O(n) space, and O(n) preprocessing-time algorithm is practically the most efficient among the tested algorithms.

AB - The point-location problem is stated as follows: Given a subdivision of the plane by a straight line planer graph G with n vertices and an arbitrary query point Q, determine which region of the subdivision contains Q. A new practical point-location algorithm is proposed. It has 0(1) search time, O(n) space, and O(n) preprocessing time in the average case. Existing point-location algorithms, as well as the one proposed here, have been implemented in FORTRAN, and their practical efficiencies are investigated by computational experiments on several planar subdivisions defined by graphs with 200-4000 vertices. It is shown that our 0(1) search-time, O(n) space, and O(n) preprocessing-time algorithm is practically the most efficient among the tested algorithms.

KW - bucketing

KW - Computational complexity

KW - computational geometry

KW - multidimensional search

KW - planar graphs

KW - point location

KW - VLSI design

UR - http://www.scopus.com/inward/record.url?scp=0346233742&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346233742&partnerID=8YFLogxK

U2 - 10.1145/357337.357338

DO - 10.1145/357337.357338

M3 - Article

AN - SCOPUS:0346233742

VL - 3

SP - 86

EP - 109

JO - ACM Transactions on Graphics

JF - ACM Transactions on Graphics

SN - 0730-0301

IS - 2

ER -