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Optimal placement of convex polygons to maximize point containment
1998
Computational geometry
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Given a convex polygon P with m vertices and a set S of n points in the plane, we consider the problem of finding a placement of P (allowing both translation and rotation) that contains the maximum number ...
We then give a refinement that makes use of bucketing to improve the running time to O(nk2c2m 2 log(mk)), where c is the ratio of length to width of the polygon. ...
Problem 1 (Optimal polygon placement). Given a convex polygon P and a planar point set S, find a rigid motion p that maximizes the number of points contained by p(P). ...
doi:10.1016/s0925-7721(98)00015-7
fatcat:ufd2ndz4rrdcxaeinndanjwiv4
Offset-polygon annulus placement problems
[chapter]
1997
Lecture Notes in Computer Science
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Optimization criteria include both maximizing the number of points contained in a fixed size annulus and minimizing the size of the annulus needed to contain all points. ...
We address the following variants of the problem: placement of an annulus of a convex polygon as well as of a simple polygon; placement by translation only, or by translation and rotation; off-line and ...
Given a set S of n points in the plane, a convex polygon P, and a distance 6, find a placement r of P that maximizes the number of points of S contained in the 3-annulus region of r(P). ...
doi:10.1007/3-540-63307-3_76
fatcat:bdtxt4xjqrf63pgunhlop4ithu
Offset-polygon annulus placement problems
1998
Computational geometry
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Optimization criteria include both maximizing the number of points contained in a fixed size annulus and minimizing the size of the annulus needed to contain all points. ...
We address the following variants of the problem: placement of an annulus of a convex polygon as well as of a simple polygon; placement by translation only, or by translation and rotation; off-line and ...
Given a set S of n points in the plane, a convex polygon P, and a distance 6, find a placement r of P that maximizes the number of points of S contained in the 3-annulus region of r(P). ...
doi:10.1016/s0925-7721(98)00025-x
fatcat:vjiqvmj4yvcwzjsou7qadbdzye
On Some Optimization Problems in Obnoxious Facility Location
[chapter]
2000
Lecture Notes in Computer Science
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We present a general method using Voronoi diagrams to approximately solve two such problems when the sites S's are points and weighted convex polygons (correspondingly, Vm's are points and weighted points ...
Our algorithms run in polynomial time and approximate the optimal solutions of the above two problems by a factor of 2. ...
Given a convex polygonal domain P and a set of point sites S in P , find the location of m undesirable or obnoxious facilities in P , which consist of a point set V m , so as to Maximize {d(V m , V m ∪ ...
doi:10.1007/3-540-44968-x_32
fatcat:pznim24jvfexfhdfq4o7jxieiq
Translating a convex polygon to contain a maximum number of points
1997
Computational geometry
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Given a set S of n points in the plane and a convex polygon P with m vertices, we consider the problem of finding a translation of P that contains the maximum number of points in S. ...
The algorithms also solve in the same running time the bichromatic variant of the problem, where we are given two point sets A and B and the goal is to maximize the number of points covered from A while ...
Given a convex polygon P and a planar point set S, find a translation 7-that maximizes the number of points of S contained by T(P). We present two algorithms to solve Problem 1. ...
doi:10.1016/s0925-7721(96)00011-9
fatcat:5qtf3daakncwdetzg6bqhi7sym
Optimizing a constrained convex polygonal annulus
2005
Journal of Discrete Algorithms
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Given a convex polygon P and a planar point set S, the goal is to find the thinnest annulus region of P containing S. ...
We also provide solutions to a related known problem: finding the smallest homothetic copy of a polygon containing a set of points. ...
Many thanks are also due to an anonymous referee for meticulously reading this manuscript and for many suggestions to improve it. ...
doi:10.1016/j.jda.2003.12.004
fatcat:suqjchhkyzeljpfavzrsi625am
Computing the Maximum Overlap of Two Convex Polygons under Translations
1998
Theory of Computing Systems
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Let P be a convex polygon in the plane with n vertices and let Q beaconvex polygon with m vertices. ...
We prove that the maximum numberofcombinatorially distinct placements of Q with respect to P under translations is O(n 2 +m 2 + m i n (nm 2 +n 2 m)), and we g i v e an example showing that this bound is ...
Thanks to H. Alt for helpful discussions about the centroid problem. ...
doi:10.1007/pl00005845
fatcat:nmdwr7ujfveknpnqsfr72qdype
Computing the maximum overlap of two convex polygons under translations
[chapter]
1996
Lecture Notes in Computer Science
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Let P be a convex polygon in the plane with n vertices and let Q beaconvex polygon with m vertices. ...
We prove that the maximum numberofcombinatorially distinct placements of Q with respect to P under translations is O(n 2 +m 2 + m i n (nm 2 +n 2 m)), and we g i v e an example showing that this bound is ...
Thanks to H. Alt for helpful discussions about the centroid problem. ...
doi:10.1007/bfb0009488
fatcat:xraqhqwbfndc5bc6cqe6n2lsyi
The Discrete Voronoi Game in a Simple Polygon
[chapter]
2013
Lecture Notes in Computer Science
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The objective of each player is to maximize the number of users they serve. ...
Let P be a simple polygon with m vertices and let U be a set of n points in P . We consider the points of U to be "users". We consider a game with two players P1 and P2. ...
Consider any optimal placement s for P 2 . Let γ be the cell that contains s. From the previous discussion, any point in γ acts as an optimal placement for . 3 . ...
doi:10.1007/978-3-642-38768-5_19
fatcat:fkenrobs5rboxfhcyrhowy4mua
Simulated Annealing with Adaptive Neighborhood Applied to the Placement over Containers with Fixed Dimensions
2008
IFAC Proceedings Volumes
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This work deals with the problem of minimizing the waste of space that occurs on a rotational placement of a set of irregular bi-dimensional items inside a bi-dimensional container. ...
The rotation applied and the translation of the polygon are continuous parameters, and the sequence of placement is represented as a set of discrete parameters. ...
It can be defined as the problem of, given a container (a convex or concave polygon) and a set of n items (convex or concave polygons), determine the subset of items and transformations (translations and ...
doi:10.3182/20081205-2-cl-4009.00020
fatcat:azcosb2zfrg3dcrsdvdx7itigq
A Flexible Framework for Covering and Partitioning Problems in Indoor Spaces
2020
ISPRS International Journal of Geo-Information
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We apply it to particular applications, device placement and route planning problems, in order to give examples of the use of our framework in the perspective on how to design a constraint and how to use ...
In this paper, we propose a multi-stage framework for indoor space partitioning, each stage of which can be flexibly adjusted according to target applications. ...
Conflicts of Interest: The authors declare no conflict of interest. ...
doi:10.3390/ijgi9110618
fatcat:knzvfzosjncqrpt5tbfrmpdtgy
Optimized Packing Clusters of Objects in a Rectangular Container
2019
Mathematical Problems in Engineering
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A packing (layout) problem for a number of clusters (groups) composed of convex objects (e.g., circles, ellipses, or convex polygons) is considered. ...
The objective of optimized packing is constructing a maximum sparse layout for clusters subject to nonoverlapping and containment conditions for clusters and objects. ...
Conflicts of Interest The authors declare that there are no conflicts of interest regarding the publication of this paper. ...
doi:10.1155/2019/4136430
fatcat:2pxnkh3iwfggzi5dg76jyenszm
Improving the Reliability and Availability of Vehicular Communications Using Voronoi Diagram-Based Placement of Road Side Units
2012
2012 IEEE 31st Symposium on Reliable Distributed Systems
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Effective placement of the RSUs is a key requirement in improving reliability of VANET services. This poster describes a novel Voronoi network-based algorithm for the effective placement of RSUs. ...
The reliability of VANET-based services and applications that are based solely on vehicle-to-vehicle (V2V) communications, however, is hindered due primarily to limited and often fluctuating V2V communications ...
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. ...
doi:10.1109/srds.2012.39
dblp:conf/srds/PatilG12
fatcat:taes64hgnvdnxg54uawsokaruq
Optimal Camera Pose and Placement Configuration for Maximum Field-of-View Video Stitching
2018
Sensors
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An optimal camera placement problem is investigated. The objective is to maximize the area of the field of view (FoV) of a stitched video obtained by stitching video streams from an array of cameras. ...
We present a method to find a convex polygon with maximum area from a given polygon. ...
Conflicts of Interest: The authors declare no conflicts of interest. ...
doi:10.3390/s18072284
pmid:30011930
pmcid:PMC6068806
fatcat:c2bwymvyhben5nw36dgiremkti
Page 7003 of Mathematical Reviews Vol. , Issue 96k
[page]
1996
Mathematical Reviews
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The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
log Q) time.”
96k:68192 68U05 52B55 Dickerson, Matthew (1-MDLC-CS; Middlebury, VT); Scharstein, Daniel (1-CRNL-C; Ithaca, NY) Optimal placement of convex polygons to maximize point containment. ...
with m vertices and a set S of n points in the plane, we consider the problem of finding a placement of P that contains the maximum number of points in S. We allow both translation and rotation. ...
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