Results 1  10
of
140
Global Optimization Algorithms  Theory and Application
, 2011
"... This ebook is devoted to Global Optimization algorithms, which are methods for finding solutions of high quality for an incredible wide range of problems. We introduce the basic concepts of optimization and discuss features which make optimization problems difficult and thus, should be considered ..."
Abstract

Cited by 94 (26 self)
 Add to MetaCart
This ebook is devoted to Global Optimization algorithms, which are methods for finding solutions of high quality for an incredible wide range of problems. We introduce the basic concepts of optimization and discuss features which make optimization problems difficult and thus, should be considered when trying to solve them. In this book, we focus on
Maximizing the Overlap of Two Planar Convex Sets under Rigid Motions
, 2006
"... Given two compact convex sets P and Q in the plane, we compute an image of P under a rigid motion that approximately maximizes the overlap with Q. More precisely, for any ε> 0, we compute a rigid motion such that the area of overlap is at least 1−ε times the maximum possible overlap. Our algorith ..."
Abstract

Cited by 11 (5 self)
 Add to MetaCart
Given two compact convex sets P and Q in the plane, we compute an image of P under a rigid motion that approximately maximizes the overlap with Q. More precisely, for any ε> 0, we compute a rigid motion such that the area of overlap is at least 1−ε times the maximum possible overlap. Our algorithm uses O(1/ε) extreme point and line intersection queries on P and Q, plus O((1/ε 2) log(1/ε)) running time. If only translations are allowed, the extra running time reduces to O((1/ε) log(1/ε)). If P and Q are convex polygons with n vertices in total that are given in an array or balanced tree, the total running time is O((1/ε) log n + (1/ε 2) log(1/ε)) for rigid motions and O((1/ε) log n + (1/ε) log(1/ε)) for translations.
Building Bridges Between Convex Regions
, 2001
"... In the Euclidean traveling salesman and buyers problem (TSBP), we are given a set of convex regions in ddimensional space, and we wish to find a minimumcost tour that visits all the regions. The cost of a tour depends on the length of the tour itself and on the distance that buyers within each ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
In the Euclidean traveling salesman and buyers problem (TSBP), we are given a set of convex regions in ddimensional space, and we wish to find a minimumcost tour that visits all the regions. The cost of a tour depends on the length of the tour itself and on the distance that buyers within each region need to travel to meet the salesman. We show that constantfactor approximations to the TSBP and several similar problems can be obtained by visiting the centers of the smallest enclosing spheres of the regions.
Optimal Empty PseudoTriangles in a Point Set
, 2009
"... Given n points in the plane, we study three optimization problems of computing an empty pseudotriangle: we consider minimizing the perimeter, maximizing the area, and minimizing the longest maximal concave chain. We consider two versions of the problem: First, we assume that the three convex vertic ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Given n points in the plane, we study three optimization problems of computing an empty pseudotriangle: we consider minimizing the perimeter, maximizing the area, and minimizing the longest maximal concave chain. We consider two versions of the problem: First, we assume that the three convex vertices of the pseudotriangle are given. Let n denote the number of points that lie inside the convex hull of the three given vertices, we can compute the minimum perimeter or maximum area pseudotriangle in O(n³) time. We can compute the pseudotriangle with minimum longest concave chain in O(n² log n) time. If the convex vertices are not given, we achieve running times of O(n log n) for minimum perimeter, O(n 6) for maximum area, and O(n² log n) for minimum longest concave chain. In any case, we use only linear space.
Bridging Convex Regions and Related Problems
"... this paper, we call the center of the minimum enclosing sphere of a region the center of the region. Since our algorithms use only the centers of regions, they can be applied to the convex regions whose centers are given or can be computed efficiently. For convex polytopes, the set of the centers c ..."
Abstract
 Add to MetaCart
this paper, we call the center of the minimum enclosing sphere of a region the center of the region. Since our algorithms use only the centers of regions, they can be applied to the convex regions whose centers are given or can be computed efficiently. For convex polytopes, the set of the centers can be computed in linear time [8]. For a convex region R, we denote by int(R) and R, the interior and the boundary of R, respectively. We define R = cl(R) = int(R) [ R. We also use j j to denote the sum of lengths of the edges in a path, a tour or a tree. f R (x) denotes the point in R farthest from x 2 R. If understood in the context, we will use f (x) instead of f R (x) if x 2 R. 2 Approximate bridge between two convex regions The minimum diameter bridge problem (MDBP) is formally defined as follows: Let R 1 and R 2 be two disjoint convex regions. We want to build a bridge pq of R 1 and R 2 at the position where the following function is minimized: max p 2R 1 d(p 0 p) +d(pq)+ max q 2R 2 d(qq 0 ); where d(pq) for any point p 2 R 3 denotes the Euclidean distance between p and q. If f (p) denotes the point in the same region as p and farthest from p, then the function can be simplified as follows: d( f (p)p) + d(pq) + d(q f (q)): We shall refer to the bridge (p;q) that minimizes the function as an optimal bridge of R and Q . We compute p 2approximation as follows: We compute the smallest enclosing spheres S 1 and S 2 of R 1 and R 2 , respectively. Let c 1 be the center and r 1 be the radius of S 1 . Similarly, let c 2 be the center and r 2 be the radius of S 2 . Since each region is convex, it is not difficult to see that the center of a region lies in the closure of the region. We choose the line segment c 1 c 2 as the approximate bridge. Let p = f (c 1 )c...
A survey on multidimensional access methods

, 2001
"... The extraordinary format of spatial data and the fact that there is no straightforward mapping of spatial objects from the multidimensional space to the 1dimensional space, stimulated various researchers during the past two decades to develop multidimensional access methods that facilitate effici ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
The extraordinary format of spatial data and the fact that there is no straightforward mapping of spatial objects from the multidimensional space to the 1dimensional space, stimulated various researchers during the past two decades to develop multidimensional access methods that facilitate efficient indexing of spatial objects in large databases. This survey paper tries a classification of existing multidimensional access methods, according to the types of data they are most suitable for (points or objects with spatial extent), their structure (hierarchical or flat), and their performance over spatial queries. Most of this work is based on an excellent survey paper [Gaed97]
Competitive Facility Location along a Highway
 In 7th Annual International Computing and Combinatorics Conference, volume 2108 of LNCS
, 2001
"... We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is then subdivided according to the nearestneighbor rule, and the player whose points control the larger a ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is then subdivided according to the nearestneighbor rule, and the player whose points control the larger area wins. We present a winning strategy for the second player, where the arena is a circle or a line segment. We also consider a variation where players can play more than one point at a time for the circle arena.
Results 1  10
of
140