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Minimum convex partition of a constrained point set

Thomas Fevens, Henk Meijer, David Rappaport
2001 Discrete Applied Mathematics  
In this paper, we will present 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] .  ... 
doi:10.1016/s0166-218x(00)00237-7 fatcat:o2luujqinbbh3odzwn3tnaterq

A General Framework for Modeling and Processing Optimization Queries

Michael Gibas, Ning Zheng, Hakan Ferhatosmanoglu
2007 Very Large Data Bases Conference  
We propose 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.  ... 
dblp:conf/vldb/GibasZF07 fatcat:jo4zvyg3cvby7lemnbqbibb2ci

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.  ... 

Pointed binary encompassing trees: Simple and optimal

Michael Hoffmann, Bettina Speckmann, Csaba D. Tóth
2010 Computational geometry  
Tunnel graphs Consider 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.  ... 
doi:10.1016/j.comgeo.2006.12.005 fatcat:ya5etjf7qrgw7ad576blajd6bm

Tight degree bounds for pseudo-triangulations of points

Lutz Kettner, David Kirkpatrick, Andrea Mantler, Jack Snoeyink, Bettina Speckmann, Fumihiko Takeuchi
2003 Computational geometry  
We show that every 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.  ... 
doi:10.1016/s0925-7721(02)00126-8 fatcat:ll5jfh7asvdqnpq776lwam64au

Rate partitioning for optimal quantization parameter selection in H.264 (SVC) based 4G broadcast/multicast wireless video communication

Nitin Khanna, Aditya K. Jagannatham
2011 2011 Australasian Telecommunication Networks and Applications Conference (ATNAC)  
We demonstrate that the optimal wireless link quality based BMG 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  ... 
doi:10.1109/atnac.2011.6096647 dblp:conf/itnac/KhannaJ11 fatcat:2augne62pzfv7afspruaays74u

Hardness and Approximation of Minimum Convex Partition [article]

Nicolas Grelier
2021 arXiv   pre-print
We consider the 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.  ... 
arXiv:1911.07697v3 fatcat:3k5aajdkmbeqzcwg3i6ttv3b7m

Lipschitz-inspired HALRECT Algorithm for Derivative-free Global Optimization [article]

Linas Stripinis, Remigijus Paulavičius
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.  ... 
arXiv:2205.03015v1 fatcat:ogviaxgw4fen3n7vffevf7kwte

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

Arindam Karmakar, Sasanka Roy, Sandip Das
2008 Information Processing Letters  
Our algorithm preprocesses 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.  ... 
doi:10.1016/j.ipl.2008.07.002 fatcat:sxpywoav3ra7zazyziu6yuibhm

Computing Low-Cost Convex Partitions for Planar Point Sets Based on Tailored Decompositions

Günther Eder, Martin Held, Stefan de Lorenzo, Peter Palfrader, Danny Z. Chen, Sergio Cabello
2020 International Symposium on Computational Geometry  
local optimizations for reducing the number 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  ... 
doi:10.4230/lipics.socg.2020.85 dblp:conf/compgeom/EderHLP20 fatcat:wwchje4rq5e3rmkj756avatty4

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]

Luis Barba, Prosenjit Bose, Stefan Langerman
2014 Lecture Notes in Computer Science  
We first study the case when Γ is 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.  ... 
doi:10.1007/978-3-642-54423-1_8 fatcat:ui2psgtxz5dc7pym4t5bicxoaq

Constrained Nearest Neighbor Queries [chapter]

Hakan Ferhatosmanoglu, Ioanna Stanoi, Divyakant Agrawal, Amr El Abbadi
2001 Lecture Notes in Computer Science  
In this paper we introduce the notion 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.  ... 
doi:10.1007/3-540-47724-1_14 fatcat:mikn543cozhbve7qf3qbb4flzy

On Constrained Minimum Pseudotriangulations [chapter]

Günter Rote, Cao An Wang, Lusheng Wang, Yinfeng Xu
2003 Lecture Notes in Computer Science  
In this paper, we show some properties 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.  ... 
doi:10.1007/3-540-45071-8_45 fatcat:t2de5zuwkzdvtmbprevqzw64um

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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