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Minimum convex partition of a constrained point set

2001
*
Discrete Applied Mathematics
*

In this paper, we will present

doi:10.1016/s0166-218x(00)00237-7
fatcat:o2luujqinbbh3odzwn3tnaterq
*a*polynomial time algorithm to ÿnd*a**minimum**convex**partition*with respect to*a**point**set*S where S is*constrained*to lie on the boundaries*of**a*ÿxed number*of*nested*convex*...*A**convex**partition*with respect to*a**point**set*S is*a*planar subdivision whose vertices are the*points**of*S, where the boundary*of*the unbounded outer face is the boundary*of*the*convex*hull*of*S, and ... This work is an extension*of*work presented in*a*previous paper on the*minimum*weight*convex*quadrangulation problem for*a**constrained**point**set*[3] . ...##
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A General Framework for Modeling and Processing Optimization Queries

2007
*
Very Large Data Bases Conference
*

We propose

dblp:conf/vldb/GibasZF07
fatcat:jo4zvyg3cvby7lemnbqbibb2ci
*a*general class*of*queries, model-based optimization queries, in which*a*generic model is used to define*a*wide variety*of*queries involving an optimization objective function and/or*a**set**of*... We cast such queries as members*of*the*convex*optimization (CP) model and provide*a*unified query processing framework for CP queries that I/O optimally accesses data and space*partitioning*index structures ... We find the*minimum*objective function for*partition*B and get the distance from the query*point*to the*point*where the*constrained*region and the*partition*B intersect,*point*c. ...##
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Page 2104 of Mathematical Reviews Vol. , Issue 2002C
[page]

2002
*
Mathematical Reviews
*

, ON);
Rappaport, David (3-QEN-C; Kingston, ON

*Minimum**convex**partition**of**a**constrained**point**set*. ...*A**minimum**convex**partition*is*a**convex**partition*such that the number*of*con- vex polygons is minimised. ...##
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Pointed binary encompassing trees: Simple and optimal

2010
*
Computational geometry
*

Tunnel graphs Consider

doi:10.1016/j.comgeo.2006.12.005
fatcat:ya5etjf7qrgw7ad576blajd6bm
*a**set*S*of*disjoint segments in the plane and*a**convex**partition*P (S) obtained by the above algorithm. ... They were introduced by Streinu [23] , who proved that every*minimum*pseudo-triangulation*of**a**set*S*of*n*points*consists*of*exactly n − 2 pseudo-triangles. ...##
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Tight degree bounds for pseudo-triangulations of points

2003
*
Computational geometry
*

We show that every

doi:10.1016/s0925-7721(02)00126-8
fatcat:ll5jfh7asvdqnpq776lwam64au
*set**of*n*points*in general position has*a**minimum*pseudo-triangulation whose maximum vertex degree is five. ... In addition, we demonstrate that every*point**set*in general position has*a**minimum*pseudotriangulation whose maximum face degree is four (i.e., each interior face*of*this pseudo-triangulation has at most ...*A*pseudo-triangulation for*a**set*S*of*n*points*in the plane is*a**partition**of*the*convex*hull*of*S into pseudo-triangles whose vertex*set*is exactly S. ...##
###
Rate partitioning for optimal quantization parameter selection in H.264 (SVC) based 4G broadcast/multicast wireless video communication

2011
*
2011 Australasian Telecommunication Networks and Applications Conference (ATNAC)
*

We demonstrate that the optimal wireless link quality based BMG

doi:10.1109/atnac.2011.6096647
dblp:conf/itnac/KhannaJ11
fatcat:2augne62pzfv7afspruaays74u
*partition*and the associated quantization, time-fraction parameters can be computed by solving*a*series*of**convex*objective minimization ... Hence, we propose*a*novel rate*partitioning*based scalable video (RPSV) transmission framework to overcome this limitation. ... We demonstrate that the computation*of*the optimal quantization and time-fraction parameters for rate*partitioning*reduces to the solution*of**a**set**of**constrained**convex*objective minimization problems ...##
###
Hardness and Approximation of Minimum Convex Partition
[article]

2021
*
arXiv
*
pre-print

We consider the

arXiv:1911.07697v3
fatcat:3k5aajdkmbeqzcwg3i6ttv3b7m
*Minimum**Convex**Partition*problem: Given*a**set*P*of*n*points*in the plane, draw*a*plane graph G on P, with positive*minimum*degree, such that G*partitions*the*convex*hull*of*P into*a**minimum*... This allows us to obtain*a*constant-approximation FPT algorithm for the*Minimum**Convex**Partition*Problem where the parameter is the number*of*faces. ... [6] :*Minimum**Convex**Partition*problem). Given*a**set*P*of*n*points*in the plane. ...##
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Lipschitz-inspired HALRECT Algorithm for Derivative-free Global Optimization
[article]

2022
*
arXiv
*
pre-print

*A*new

*partitioning*and sampling scheme utilizes more comprehensive information about the objective function. ...

*A*new deterministic approach combines halving (bisection) with

*a*new multi-

*point*sampling scheme in contrast to trisection and midpoint sampling used in the most existing DIRECT-type algorithms. ... Therefore, the

*set*

*of*POHs is enlarged with various size hyper-rectangles nearest the current

*minimum*

*point*. ...

##
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Fast computation of smallest enclosing circle with center on a query line segment

2008
*
Information Processing Letters
*

Our algorithm preprocesses

doi:10.1016/j.ipl.2008.07.002
fatcat:sxpywoav3ra7zazyziu6yuibhm
*a*given*set**of*n*points*P = {p 1 , p 2 , . . . , p n } such that for any query line or line segment L, it efficiently locates*a**point*c on L that minimizes the maximum distance ... Here we propose an efficient algorithm for computing the smallest enclosing circle whose center is*constrained*to lie on*a*query line segment. ...*Constrained*1-center problem Given*a**point**set*P = {p 1 , p 2 , . . . , p n } and*a*query line L, our objective is to enclose P with*a**minimum*radius circle C whose center c is*constrained*to lie on L. ...##
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Computing Low-Cost Convex Partitions for Planar Point Sets Based on Tailored Decompositions

2020
*
International Symposium on Computational Geometry
*

local optimizations for reducing the number

doi:10.4230/lipics.socg.2020.85
dblp:conf/compgeom/EderHLP20
fatcat:wwchje4rq5e3rmkj756avatty4
*of**convex*faces*of**a*decomposition. ... Our work on*minimum**convex*decompositions is based on two key components: (1) different strategies for computing initial decompositions, partly adapted to the characteristics*of*the input data, and (2) ... Introduction The task*of*the 2020 Computational Geometry Challenge -called Challenge in the sequel for the sake*of*brevity -was to compute*minimum**convex*decompositions (MCD)*of**point**sets*in the plane ...##
###
Page 4634 of Mathematical Reviews Vol. , Issue 93h
[page]

1993
*
Mathematical Reviews
*

The author presents

*a*primal-dual path-following interior*point*algorithm for*a*class*of*linearly*constrained**convex*optimiza- tion problems. ... over*a*compact*set*. ...##
###
Optimal Algorithms for Constrained 1-Center Problems
[chapter]

2014
*
Lecture Notes in Computer Science
*

We first study the case when Γ is

doi:10.1007/978-3-642-54423-1_8
fatcat:ui2psgtxz5dc7pym4t5bicxoaq
*a**set**of*n*points*and Φ is either*a**set**of**points*,*a**set**of*segments (lines) or*a*simple polygon. ... We address the following problem: Given two subsets Γ and Φ*of*the plane, find the*minimum*enclosing circle*of*Γ whose center is*constrained*to lie on Φ. ... [8] presented*a*Θ(n + m)-time algorithm to find the*minimum*P -circle whose center is*constrained*to lie inside*a**convex*m-gon. ...##
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Constrained Nearest Neighbor Queries
[chapter]

2001
*
Lecture Notes in Computer Science
*

In this paper we introduce the notion

doi:10.1007/3-540-47724-1_14
fatcat:mikn543cozhbve7qf3qbb4flzy
*of**constrained*nearest neighbor queries (CNN) and propose*a*series*of*methods to answer them. ... We prove the optimality (with respect to I/O cost)*of*one*of*the techniques proposed in this paper. The superiority*of*the proposed technique is shown by*a*performance analysis. ... We need to redefine containment*of**a**minimum*bounding rectangle into the*constraining*region. ...##
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On Constrained Minimum Pseudotriangulations
[chapter]

2003
*
Lecture Notes in Computer Science
*

In this paper, we show some properties

doi:10.1007/3-540-45071-8_45
fatcat:t2de5zuwkzdvtmbprevqzw64um
*of**a*pseudotriangle and present three combinatorial bounds: the ratio*of*the size*of**minimum*pseudotriangulation*of**a**point**set*S and the size*of*minimal pseudotriangulation ... We finally study the*minimum*pseudotriangulation containing*a*given*set**of*non-crossing line segments. ...*A*pseudotriangulation*of**a**point**set*S is*a**partition**of*the interior*of*the*convex*hull*of*S into*a**set**of*pseudotriangles. ...##
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Page 7086 of Mathematical Reviews Vol. , Issue 95k
[page]

1995
*
Mathematical Reviews
*

Summary: “

*A*unified framework is presented for studying the convergence*of*projection methods for finding*a*common*point**of*finitely many closed*convex**sets*in R”. ... Summary: “Two algorithms for finding*a*global*minimum**of*the product*of*two affine fractional functions over*a*compact*convex**set*and solving linear fractional programs with an additional con- straint ...
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