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Large bichromatic point sets admit empty monochromatic 4gons
 in Proceedings of the 25th European Workshop on Computational Geometry
, 2009
"... Large bichromatic point sets admit empty monochromatic 4gons ..."
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Cited by 5 (2 self)
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Large bichromatic point sets admit empty monochromatic 4gons
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
Empty monochromatic triangles
 COMPUTATIONAL GEOMETRY, THEORY AND APPLICATIONS
, 2008
"... We consider a variation of a problem stated by Erdös and Guy in 1973 about the number of convex kgons determined by any set S of n points in the plane. In our setting the points of S are colored and we say that a spanned polygon is monochromatic if all its points are colored with the same color. As ..."
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Cited by 7 (4 self)
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. As a main result we show that any bicolored set of n points in R 2 in general position determines a superlinear number of empty monochromatic triangles, namely Ω(n 5/4).
Empty Monochromatic Simplices
, 2012
"... Let S be a kcolored (finite) set of n points in Rd, d ≥ 3, in general position, that is, no (d+1) points of S lie in a common (d−1)dimensional hyperplane. We count the number of empty monochromatic dsimplices determined by S, that is, simplices which have only points from one color class of S as ..."
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Let S be a kcolored (finite) set of n points in Rd, d ≥ 3, in general position, that is, no (d+1) points of S lie in a common (d−1)dimensional hyperplane. We count the number of empty monochromatic dsimplices determined by S, that is, simplices which have only points from one color class
Continuous evaluation of monochromatic and bichromatic reverse nearest neighbors
 In ICDE
, 2007
"... This paper presents a novel algorithm for Incremental and General Evaluation of continuous Reverse Nearest neighbor queries (IGERN, for short). The IGERN algorithm is general as it is applicable for both the monochromatic and bichromatic reverse nearest neighbor queries. The incremental aspect of IG ..."
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Cited by 37 (5 self)
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This paper presents a novel algorithm for Incremental and General Evaluation of continuous Reverse Nearest neighbor queries (IGERN, for short). The IGERN algorithm is general as it is applicable for both the monochromatic and bichromatic reverse nearest neighbor queries. The incremental aspect
Bichromatic Quadrangulations with Steiner Points
"... Abstract. Let P be a k colored point set in general position, k ≥ 2. A family of quadrilaterals with disjoint interiors Q1,..., Qm is called a quadrangulation of P if V (Q1) ∪...∪V (Qm) = P, the edges of all Qi join points with different colors, and Q1 ∪... ∪ Qm = Conv(P). In general it is easy to ..."
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to see that not all kcolored point sets admit a quadrangulation; when they do, we call them quadrangulatable. For a point set to be quadrangulatable it must satisfy that its convex hull Conv(P) has an even number of points and that consecutive vertices of Conv(P) receive different colors
Monochromatic empty triangles in twocolored point sets
"... Improving a result of Aichholzer et. al., we show that there exists a constant c> 0 satisfying the following condition. Any twocolored set of n points in general position in the plane has at least cn 4/3 triples of the same color such that the triangles spanned by them contain no element of the ..."
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Cited by 8 (0 self)
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Improving a result of Aichholzer et. al., we show that there exists a constant c> 0 satisfying the following condition. Any twocolored set of n points in general position in the plane has at least cn 4/3 triples of the same color such that the triangles spanned by them contain no element
On the bichromatic kset problem
 Proc. 19th ACMSIAM Sympos. Discrete Algorithms
, 2008
"... Abstract We study a bichromatic version of the wellknown kset problem: given two sets R and B of points of total size n and an integer k, how many subsets of the form (R " h) [ (B n h) can have size exactly k over all halfspaces h? In the dual, the problem is asymptotically equivalent to ..."
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Cited by 5 (1 self)
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Abstract We study a bichromatic version of the wellknown kset problem: given two sets R and B of points of total size n and an integer k, how many subsets of the form (R " h) [ (B n h) can have size exactly k over all halfspaces h? In the dual, the problem is asymptotically equivalent
Results 1  10
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5,632