Smallest paths in simple rectilinear polygons
WebbSuch paths have already been studied, e.g. in [4, 9, 14, 15], where shortest rectilinear paths in the LI-metric are sought. Instead, we are interested in shortest rectilinear paths in the link distance metric. We will restrict ourselves in this paper ... Definition 1 Let P be a simple rectilinear polygon. A (rectilinear) path 7r (in P) WebbWe provide optimal parallel solutions to several link-distance problems set in trapezoided rectilinear polygons. All our main parallel algorithms are deterministic and designed to run on the exclusive read exclusive write parallel random access machine (...
Smallest paths in simple rectilinear polygons
Did you know?
Webb1 jan. 2005 · We present a data structure that allows to preprocess a rectilinear polygon such that shortest path queries in the rectilinear link or L 1 metric for any two points can … Webb20 sep. 2024 · In this paper we consider the L 1-metric inside a simple rectilinear polygon P, i.e. the distance between two points in P is defined as the length of a shortest rectilinear path connecting them.
WebbA rectilinear path is a path composed only of horizontal and vertical line segments. Such paths may be constrained by requiring that they lie only within certain areas. One way of … WebbA smallest path between two points is a rectilinear path that simultaneously minimizes distance and the number of horizontal and vertical line segments in the path. Potential applications of smallest rectilinear paths include the simultaneous minimization of vias …
Webb27 apr. 2012 · This Demonstration illustrates an algorithm for finding the shortest path that stays inside a polygon and connects two given interior points. Aside from the start and … Webb13 maj 1988 · The shortest path in the `unrolled' polygon is equivalent to the shortest route in the original polygon P. Proof. From elementary geometry, it is known that if two points (or lines) A and B are on the same side of a line (or line segment) L, then the Volume 28, Number 1 INFORMATION PROCESSING LETTERS 30 May 1388 IL (a) (d) ,ti, (c) L___J Fig. 3.
Webb7 nov. 1994 · There exists a shortest path from S to T which is not x-, y-, or xy-monotone. However, C S is the rectilinear polygon without holes, so we can use the algorithm of …
WebbSMALLEST PATHS IN POLYGONS Kenneth M. McDonald B.Sc. (Hons.), University of Saskatchewan, 1986 THESIS SUBMITTED IN PARTIAL FULFLLLMENT OF THE REQUIREMENTS FOR TI-E DEGREE OF MASTER OF SCIENCE in the School of Computing Science O Kenneth M. McDonald 1989 SIMON FRASER UNIVERSITY how can you make a newtonian telescopeWebb1 apr. 2024 · Abstract We compute shortest paths connecting two axis-aligned rectilinear simple polygons in the domain consisting of axis-aligned rectilinear obstacles in the plane. The bounding boxes, one defined for each polygon and … how many people use ms teamsWebbSmallest rectilinear paths are rectilinear paths with simultaneous minimum numbers of bends and minimum lengths. Given two pairs of terminals within a rectiline The smallest … how can you make a ring smallerWebbIt is shown that shortest-path queries can be performed optimally in time O(logh + logn) (plus O(k) time for reporting the k edges of the path) using a data structure with O(n) space and preprocessing time, and that minimum-link- path queries can also be performed in optimal time. Expand 12 PDF Save Alert how can you make a paper airplane fly fartherWebb1 mars 1999 · In this paper we present optimal sequential and parallel algorithms to compute a minimum rectilinear link path in a trapezoided region R. Our parallel algorithm requires O (log n) time using a... how many people use nearpodWebb28 mars 2024 · A minimum link path is a polygonal path between two points s and t inside a simple polygon P with n vertices that has the minimum number of links. Minimum link paths are fundamentally different from traditional Euclidean shortest path, which has the shortest length among all the polygonal paths without crossing edges of P . how can you make an appWebb1 aug. 1990 · We consider the terrain navigation problem in a two-dimensional polygonal subdivision with three types of regions: obstacles, “free” regions (in which one can travel at no cost), and regions in which cost is proportional to distance traveled. how can you make an observation