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Optimal placement of convex polygons to maximize point containment

1998
*
Computational geometry
*

Given a

doi:10.1016/s0925-7721(98)00015-7
fatcat:ufd2ndz4rrdcxaeinndanjwiv4
*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). ...##
###
Offset-polygon annulus placement problems
[chapter]

1997
*
Lecture Notes in Computer Science
*

*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). ...

##
###
Offset-polygon annulus placement problems

1998
*
Computational geometry
*

*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). ...

##
###
On Some Optimization Problems in Obnoxious Facility Location
[chapter]

2000
*
Lecture Notes in Computer Science
*

We present a general method using Voronoi diagrams

doi:10.1007/3-540-44968-x_32
fatcat:pznim24jvfexfhdfq4o7jxieiq
*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 ∪ ...##
###
Translating a convex polygon to contain a maximum number of points

1997
*
Computational geometry
*

Given a set S

doi:10.1016/s0925-7721(96)00011-9
fatcat:5qtf3daakncwdetzg6bqhi7sym
*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. ...##
###
Optimizing a constrained convex polygonal annulus

2005
*
Journal of Discrete Algorithms
*

Given a

doi:10.1016/j.jda.2003.12.004
fatcat:suqjchhkyzeljpfavzrsi625am
*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. ...##
###
Computing the Maximum Overlap of Two Convex Polygons under Translations

1998
*
Theory of Computing Systems
*

Let P be a

doi:10.1007/pl00005845
fatcat:nmdwr7ujfveknpnqsfr72qdype
*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. ...##
###
Computing the maximum overlap of two convex polygons under translations
[chapter]

1996
*
Lecture Notes in Computer Science
*

Let P be a

doi:10.1007/bfb0009488
fatcat:xraqhqwbfndc5bc6cqe6n2lsyi
*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. ...##
###
The Discrete Voronoi Game in a Simple Polygon
[chapter]

2013
*
Lecture Notes in Computer Science
*

The objective

doi:10.1007/978-3-642-38768-5_19
fatcat:fkenrobs5rboxfhcyrhowy4mua
*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 . ...##
###
Simulated Annealing with Adaptive Neighborhood Applied to the Placement over Containers with Fixed Dimensions

2008
*
IFAC Proceedings Volumes
*

This work deals with the problem

doi:10.3182/20081205-2-cl-4009.00020
fatcat:azcosb2zfrg3dcrsdvdx7itigq
*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 ...##
###
A Flexible Framework for Covering and Partitioning Problems in Indoor Spaces

2020
*
ISPRS International Journal of Geo-Information
*

We apply it

doi:10.3390/ijgi9110618
fatcat:knzvfzosjncqrpt5tbfrmpdtgy
*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. ...##
###
Optimized Packing Clusters of Objects in a Rectangular Container

2019
*
Mathematical Problems in Engineering
*

A packing (layout) problem for a number

doi:10.1155/2019/4136430
fatcat:2pxnkh3iwfggzi5dg76jyenszm
*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. ...##
###
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
*

Effective

doi:10.1109/srds.2012.39
dblp:conf/srds/PatilG12
fatcat:taes64hgnvdnxg54uawsokaruq
*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. ...##
###
Optimal Camera Pose and Placement Configuration for Maximum Field-of-View Video Stitching

2018
*
Sensors
*

An

doi:10.3390/s18072284
pmid:30011930
pmcid:PMC6068806
fatcat:c2bwymvyhben5nw36dgiremkti
*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. ...##
###
Page 7003 of Mathematical Reviews Vol. , Issue 96k
[page]

1996
*
Mathematical Reviews
*

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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