Journal ArticleDOI
Voronoi Diagrams in L1 (L∞) Metrics with 2-Dimensional Storage Applications
Der-Tsai Lee,C. K. Wong +1 more
TLDR
It is shown in this paper that there exists a natural isometry between the L_1 and L_\infty metrics, which implies the existence of a polynomial time algorithm for the OPP in one metric and the existence for the same problem in the other metric.Abstract:
In this paper we study the problem of scheduling the read/write head movement to handle a batch of $nI/O$ requests in a 2-dimensional secondary storage device in minimum time. Two models of storage systems are assumed in which the access time of a record (being proportional to the “distance” between the position of the record and that of the read/write head) is measured in terms of $L_1 $ and $L_\infty $ metrics, respectively. The scheduling problem, referred to as the Open Path Problem (OPP), is equivalent to finding a shortest Hamiltonian path with a specified end point in a complete graph with n vertices. We first show in this paper that there exists a natural isometry between the $L_1 $ and $L_\infty $ metrics. Consequently, the existence of a polynomial time algorithm for the OPP in one metric implies the existence of a polynomial time algorithm for the same problem in the other metric. Based on a result by Garey, Graham and Johnson, it is easy to show that the OPP in $L_1 $ (hence in $L_\infty $) me...read more
Citations
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Journal ArticleDOI
Voronoi diagrams—a survey of a fundamental geometric data structure
TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
Proceedings ArticleDOI
Scaling and related techniques for geometry problems
TL;DR: Three techniques in computational geometry are explored: scaling solves a problem by viewing it at increasing levels of numerical precision; activation is a restricted type of update operation, useful in sweep algorithms; the Cartesian tree is a data structure for problems involving maximums and minimums.
Journal ArticleDOI
Steiner tree problems
Frank K. Hwang,Dana Richards +1 more
TL;DR: A survey up to 1989 on the Steiner tree problems which include the four important cases of euclidean, rectilinear, graphic, phylogenetic and some of their generalizations.
Journal ArticleDOI
Voronoi diagrams and arrangements
TL;DR: It turns out that the standard Euclidean Voronoi diagram of point sets inRd along with its order-k generalizations are intimately related to certain arrangements of hyperplanes, and this fact can be used to obtain new Vor onoi diagram algorithms.
Journal ArticleDOI
AnO(n logn) algorithm for the voronoi diagram of a set of simple curve segments
TL;DR: A new technique is introduced that computes the Voronoi diagram ofX inO(n logn) time, which improves on several previous algorithms for special cases of the problem.
References
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The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Journal ArticleDOI
Rectilinear steiner trees: Efficient special‐case algorithms
TL;DR: Two algorithms are presented, each requiring a number of operations proportional to only a low degree polynomial in the number of points to be interconnected, for the special cases in which all the points of A lie on a small number of parallel lines or on the boundary of a rectangle.
Journal ArticleDOI
Near-Optimal Solutions to a 2-Dimensional Placement Problem
TL;DR: This work considers the problem of placing records in a 2-dimensional storage array so that expected distance between consecutive references is minimized and a simple placement heuristic which uses only relative frequency of access for different records is shown to be within an additive constant of optimal when distance is measured by the Euclidean metric.