TY - GEN
T1 - Applications of parametric searching in geometric optimization
AU - Agarwal, Pankaj K.
AU - Sharir, Micha
AU - Toledo, Sivan
N1 - Funding Information:
*Pankaj Agarwal has been supported by National Science Foundation Grant CCR-91-06514. Micha Sharir has been supported by Office of Naval Research Grant NOO014-90-.J-1284, by Nationaf Science Foundation Grant CCR-89-01484, and by grants from the U.S.–Israeli Binationaf Science Foundation, the G.I.F. — the German Israeli Foundation for Scientific Research and Development, and the Fund for Basic Research administered by the Israeli Academy of Sciences. Sivan Toledo has been supported by the Special Interdisciplinary Program at Tel-Aviv University. t Department of Computer Science, Duke University. $Cour-t Institute of Mathematical Sciences, New York University, and School of Mathematical Sciences, Tel Aviv University.
PY - 1992/9/1
Y1 - 1992/9/1
N2 - We present several applications in computational geometry of Megiddo's parametric searching technique. These applications include: (1) Finding the minimum Hausdorff distance in the Euclidean metric between two polygonal regions under translation; (2) Computing the biggest line segment that can be placed inside a simple polygon; (3) Computing the smallest width annulus that can contain a given set of points in the plane; (4) Solving the 1-segment center problem - given a set of points in the plane, find a placement for a given line segment (under translation and rotation) which minimizes the largest distance from the segment to the given points; (5) Given a set of n points in 3-space, rinding the largest radius r such that if we place a ball of radius r around each point, no segment connecting a pair of points is intersected by a third ball. Besides obtaining efficient solutions to all these problems (which, in every case, either improve considerably previous solutions or are the first non-trivial solutions to these problems), our goal is to demonstrate the versatility of the parametric searching technique.
AB - We present several applications in computational geometry of Megiddo's parametric searching technique. These applications include: (1) Finding the minimum Hausdorff distance in the Euclidean metric between two polygonal regions under translation; (2) Computing the biggest line segment that can be placed inside a simple polygon; (3) Computing the smallest width annulus that can contain a given set of points in the plane; (4) Solving the 1-segment center problem - given a set of points in the plane, find a placement for a given line segment (under translation and rotation) which minimizes the largest distance from the segment to the given points; (5) Given a set of n points in 3-space, rinding the largest radius r such that if we place a ball of radius r around each point, no segment connecting a pair of points is intersected by a third ball. Besides obtaining efficient solutions to all these problems (which, in every case, either improve considerably previous solutions or are the first non-trivial solutions to these problems), our goal is to demonstrate the versatility of the parametric searching technique.
UR - http://www.scopus.com/inward/record.url?scp=84969379775&partnerID=8YFLogxK
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AN - SCOPUS:84969379775
T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
SP - 72
EP - 82
BT - Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992
PB - Association for Computing Machinery
T2 - 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992
Y2 - 27 January 1992 through 29 January 1992
ER -