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EMPTY PENTAGONS IN POINT SETS WITH COLLINEARITIES
"... Abstract. An empty pentagon in a point set P in the plane is a set of five points in P in strictly convex position with no other point of P in their convex hull. We prove that every finite set of at least 328`2 points in the plane contains an empty pentagon or ` collinear points. This is optimal up ..."
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Abstract. An empty pentagon in a point set P in the plane is a set of five points in P in strictly convex position with no other point of P in their convex hull. We prove that every finite set of at least 328`2 points in the plane contains an empty pentagon or ` collinear points. This is optimal up
EMPTY PENTAGONS IN POINT SETS WITH COLLINEARITIES
, 1207
"... Abstract. An empty pentagon in a point set P in the plane is a set of five points in P in strictly convex position with no other point of P in their convex hull. We prove that every finite set of at least 328ℓ 2 points in the plane contains an empty pentagon or ℓ collinear points. This is optimal up ..."
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Cited by 2 (1 self)
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Abstract. An empty pentagon in a point set P in the plane is a set of five points in P in strictly convex position with no other point of P in their convex hull. We prove that every finite set of at least 328ℓ 2 points in the plane contains an empty pentagon or ℓ collinear points. This is optimal
EVERY LARGE POINT SET CONTAINS MANY COLLINEAR POINTS OR AN EMPTY PENTAGON
, 2009
"... We prove the following generalised empty pentagon theorem: for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood ..."
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Cited by 12 (4 self)
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We prove the following generalised empty pentagon theorem: for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór
OPTICS: Ordering Points To Identify the Clustering Structure
, 1999
"... Cluster analysis is a primary method for database mining. It is either used as a standalone tool to get insight into the distribution of a data set, e.g. to focus further analysis and data processing, or as a preprocessing step for other algorithms operating on the detected clusters. Almost all of ..."
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Cited by 511 (49 self)
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.g. representative points, arbitrary shaped clusters), but also the intrinsic clustering structure. For medium sized data sets, the clusterordering can be represented graphically and for very large data sets, we introduce an appropriate visualization technique. Both are suitable for interactive exploration
Iterative point matching for registration of freeform curves and surfaces
, 1994
"... A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in ma ..."
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Cited by 659 (7 self)
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, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points
QSplat: A Multiresolution Point Rendering System for Large Meshes
, 2000
"... Advances in 3D scanning technologies have enabled the practical creation of meshes with hundreds of millions of polygons. Traditional algorithms for display, simplification, and progressive transmission of meshes are impractical for data sets of this size. We describe a system for representing and p ..."
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Cited by 500 (8 self)
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Advances in 3D scanning technologies have enabled the practical creation of meshes with hundreds of millions of polygons. Traditional algorithms for display, simplification, and progressive transmission of meshes are impractical for data sets of this size. We describe a system for representing
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 511 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 then almost surely all components in such graphs are small. We can apply these results to G n;p ; G n;M , and other wellknown models of random graphs. There are also applications related to the chromatic number of sparse random graphs.
Mining Association Rules between Sets of Items in Large Databases
 IN: PROCEEDINGS OF THE 1993 ACM SIGMOD INTERNATIONAL CONFERENCE ON MANAGEMENT OF DATA, WASHINGTON DC (USA
, 1993
"... We are given a large database of customer transactions. Each transaction consists of items purchased by a customer in a visit. We present an efficient algorithm that generates all significant association rules between items in the database. The algorithm incorporates buffer management and novel esti ..."
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Cited by 3260 (17 self)
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We are given a large database of customer transactions. Each transaction consists of items purchased by a customer in a visit. We present an efficient algorithm that generates all significant association rules between items in the database. The algorithm incorporates buffer management and novel estimation and pruning techniques. We also present results of applying this algorithm to sales data obtained from a large retailing company, which shows the effectiveness of the algorithm.
The Skyline Operator
 IN ICDE
, 2001
"... We propose to extend database systems by a Skyline operation. This operation filters out a set of interesting points from a potentially large set of data points. A point is interesting if it is not dominated by any other point. For example, a hotel might be interesting for somebody traveling to Nass ..."
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Cited by 558 (3 self)
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We propose to extend database systems by a Skyline operation. This operation filters out a set of interesting points from a potentially large set of data points. A point is interesting if it is not dominated by any other point. For example, a hotel might be interesting for somebody traveling
Results 1  10
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