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Algorithms for Maximum Independent Set Applied to Map Labelling
, 2000
"... We consider the following map labelling problem: given distinct points p 1 , p 2 , . . . , p n in the plane, and given #, find a maximum cardinality set of pairwise disjoint axisparallel # # squares Q 1 , Q 2 , . . . , Q r . This problem reduces to that of finding a maximum cardinality indepe ..."
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Cited by 18 (0 self)
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We consider the following map labelling problem: given distinct points p 1 , p 2 , . . . , p n in the plane, and given #, find a maximum cardinality set of pairwise disjoint axisparallel # # squares Q 1 , Q 2 , . . . , Q r . This problem reduces to that of finding a maximum cardinality
On the Proper Learning of AxisParallel Concepts
 Journal of Machine Learning Research
, 2003
"... We study the proper learnability of axisparallel concept classes in the PAClearning and exactlearning models. These classes include union of boxes, DNF, decision trees and multivariate polynomials. For constantdimensional axisparallel concepts C we show that the following problems have time comp ..."
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Cited by 1 (0 self)
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We study the proper learnability of axisparallel concept classes in the PAClearning and exactlearning models. These classes include union of boxes, DNF, decision trees and multivariate polynomials. For constantdimensional axisparallel concepts C we show that the following problems have time
Alternating Paths along Axisparallel Segments
, 2003
"... It is shown that for a set S of n pairwise disjoint axisparallel line segments in the plane there is a simple alternating path of length Ω(√n). This bound is best possible in the worst case. In the special case that the n pairwise disjoint axisparallel line segments are protruded (that is, if the ..."
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Cited by 2 (1 self)
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It is shown that for a set S of n pairwise disjoint axisparallel line segments in the plane there is a simple alternating path of length Ω(√n). This bound is best possible in the worst case. In the special case that the n pairwise disjoint axisparallel line segments are protruded (that is
On Point Covers Of Multiple Intervals And Axisparallel Rectangles
, 1995
"... In certain families of hypergraphs the transversal number is bounded by some function of the packing number. In this paper we study hypergraphs related to multiple intervals and axisparallel rectangles, respectively. Essential improvements of former established upper bounds are presented here. We e ..."
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Cited by 6 (0 self)
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In certain families of hypergraphs the transversal number is bounded by some function of the packing number. In this paper we study hypergraphs related to multiple intervals and axisparallel rectangles, respectively. Essential improvements of former established upper bounds are presented here. We
Binary Space Partitions for AxisParallel Segments, Rectangles, and Hyperrectangles
 IN PROC. 17TH ANNU. ACM SYMPOS. COMPUT. GEOM
, 2001
"... We provide a variety of new results, including upper and lower bounds, as well as simpler proof techniques for the ecient construction of binary space partitions (BSP's) of axisparallel segments, rectangles, and hyperrectangles. (a) A consequence of the analysis in [1] is that any set of n axi ..."
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Cited by 19 (1 self)
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axisparallel and pairwisedisjoint line segments in the plane admits a binary space partition of size at most 2n 1. We establish a worstcase lower bound of 2n o(n) for the size of such a BSP, thus showing that this bound is almost tight in the worst case. (b) We give an improved worstcase lower
PAIRWISE
"... Let K be a set of positive integers. A pairwise balanced design (PBD) of index unity B(K,l;v) is a pair (X/~) where X is a vset (of points) and B is a collection of subsets of X (called blocks) with sizes from K such that every pair of distinct points of X is contained in exactly one block of~. A n ..."
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Let K be a set of positive integers. A pairwise balanced design (PBD) of index unity B(K,l;v) is a pair (X/~) where X is a vset (of points) and B is a collection of subsets of X (called blocks) with sizes from K such that every pair of distinct points of X is contained in exactly one block of~. A
Finding the Maximum Area AxisParallel Rectangle in a Polygon
, 1993
"... We consider the geometric optimization problem of finding the maximum area axisparallel rectangle (MAAPR) in an nvertex general polygon. We characterize the MAAPR for general polygons by considering different cases based on the types of contacts between the rectangle and the polygon. We present a ..."
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Cited by 6 (2 self)
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We consider the geometric optimization problem of finding the maximum area axisparallel rectangle (MAAPR) in an nvertex general polygon. We characterize the MAAPR for general polygons by considering different cases based on the types of contacts between the rectangle and the polygon. We present a
Matching Points into PairwiseDisjoint Noise Regions: Combinatorial Bounds and Algorithms
 ORSA J. Comput
, 1992
"... We consider several cases of the point matching problem in which we are to find a transformation of a set of n points such that each transformed point lies in one of n given pairwisedisjoint "noise regions". We prove upper and lower bounds on the number of possible matches, under a variet ..."
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Cited by 7 (3 self)
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We consider several cases of the point matching problem in which we are to find a transformation of a set of n points such that each transformed point lies in one of n given pairwisedisjoint "noise regions". We prove upper and lower bounds on the number of possible matches, under a
Steiner Triple Systems Intersecting in Pairwise Disjoint Blocks
 Electronic J. Combin
"... Two Steiner triple systems (X,A)and(X,B) are said to intersect in m pairwise disjoint blocks if A # B = m and all blocks in A#B are pairwise disjoint. For each v, we completely determine the possible values of m such that there exist two Steiner triple systems of order v intersecting in m pair ..."
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Cited by 5 (3 self)
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Two Steiner triple systems (X,A)and(X,B) are said to intersect in m pairwise disjoint blocks if A # B = m and all blocks in A#B are pairwise disjoint. For each v, we completely determine the possible values of m such that there exist two Steiner triple systems of order v intersecting in m
Active SemiSupervision for Pairwise Constrained Clustering
 Proc. 4th SIAM Intl. Conf. on Data Mining (SDM2004
"... Semisupervised clustering uses a small amount of supervised data to aid unsupervised learning. One typical approach specifies a limited number of mustlink and cannotlink constraints between pairs of examples. This paper presents a pairwise constrained clustering framework and a new method for acti ..."
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Cited by 134 (9 self)
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Semisupervised clustering uses a small amount of supervised data to aid unsupervised learning. One typical approach specifies a limited number of mustlink and cannotlink constraints between pairs of examples. This paper presents a pairwise constrained clustering framework and a new method
Results 1  10
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