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Automatic Subspace Clustering of High Dimensional Data
 Data Mining and Knowledge Discovery
, 2005
"... Data mining applications place special requirements on clustering algorithms including: the ability to find clusters embedded in subspaces of high dimensional data, scalability, enduser comprehensibility of the results, nonpresumption of any canonical data distribution, and insensitivity to the or ..."
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Cited by 560 (12 self)
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Data mining applications place special requirements on clustering algorithms including: the ability to find clusters embedded in subspaces of high dimensional data, scalability, enduser comprehensibility of the results, nonpresumption of any canonical data distribution, and insensitivity to the order of input records. We present CLIQUE, a clustering algorithm that satisfies each of these requirements. CLIQUE identifies dense clusters in subspaces of maximum dimensionality. It generates cluster descriptions in the form of DNF expressions that are minimized for ease of comprehension. It produces identical results irrespective of the order in which input records are presented and does not presume any specific mathematical form for data distribution. Through experiments, we show that CLIQUE efficiently finds accurate clusters in large high dimensional datasets.
Covering Rectilinear Polygons with AxisParallel Rectangles
, 1999
"... We give an O(sqrt(log n)) factor approximation algorithm for covering a rectilinear polygon with holes using axisparallel rectangles. This is the first polynomial time approximation algorithm for this problem with a o(log n) approximation factor. ..."
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Cited by 26 (1 self)
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We give an O(sqrt(log n)) factor approximation algorithm for covering a rectilinear polygon with holes using axisparallel rectangles. This is the first polynomial time approximation algorithm for this problem with a o(log n) approximation factor.
Close Approximations of Minimum Rectangular Coverings
 In FST & TCS'96, volume 1180 of LNCS
, 1996
"... . We consider the problem of covering arbitrary polygons with rectangles. The rectangles must lie entirely within the polygon. (This requires that the interior angles of the polygon are all greater than or equal to 90 degrees.) We want to cover the polygon with as few rectangles as possible. Thi ..."
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Cited by 7 (2 self)
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. We consider the problem of covering arbitrary polygons with rectangles. The rectangles must lie entirely within the polygon. (This requires that the interior angles of the polygon are all greater than or equal to 90 degrees.) We want to cover the polygon with as few rectangles as possible. This problem has an application in fabricating masks for integrated circuits. In this paper we will describe the first polynomial algorithm, guaranteeing an O(log n) approximation factor, provided that the n vertices of the input polygon are given as polynomially bounded integer coordinates. By the same technique we also obtain the first algorithm producing a covering which is within a constant factor of the optimal in exponential time (compared to the doublyexponential known before). 1 Introduction The problem of covering polygons with various types of simpler polygons has a number of important practical applications [5, 6] and has received considerable attention from a theoretical p...
Applying Partial Evaluation to VLSI Design Rule Checking
, 1995
"... This report describes the design and implementation of a complete VLSI design rule checking program. We use formal techniques to develop a methodology for performing design rule checking, and implement this methodology in the Scheme programming language. We specify the requirements for a simplified ..."
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Cited by 2 (0 self)
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This report describes the design and implementation of a complete VLSI design rule checking program. We use formal techniques to develop a methodology for performing design rule checking, and implement this methodology in the Scheme programming language. We specify the requirements for a simplified VLSI design database and implement it, making use of the Hilbert Rtree. We describe the implementationof an efficient algorithm for the decompositionof rectilinear polygons into collections of rectangles. We apply partial evaluation techniques to our final design rule checking program in order to determine the effect this has on our program's structure and performance. Finally, we describe the implementation of a graphical user interface for the checker and summarise our experiences and insights gained during the course of this project. Acknowledgement I would like to thank my supervisor, Dr. Andrew Butterfield, for his suggestions and support during this project. I would also like to th...
Two Geometric Optimization Problems
 in DingZhu Du and Jie Sun (eds.), New Advances in Optimization and Approximation
, 1994
"... . We consider two optimization problems with geometric structures. The first one concerns the following minimization problem, termed as the rectilinear polygon cover problem: "Cover certain features of a given rectilinear polygon (possibly with rectilinear holes) with the minimum number of rectangle ..."
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Cited by 1 (0 self)
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. We consider two optimization problems with geometric structures. The first one concerns the following minimization problem, termed as the rectilinear polygon cover problem: "Cover certain features of a given rectilinear polygon (possibly with rectilinear holes) with the minimum number of rectangles included in the polygon." Depending upon whether one wants to cover the interior, boundary or corners of the polygon, the problem is termed as the interior, boundary or corner cover problem, respectively. Most of these problems are known to be NPcomplete. In this chapter we survey some of the important previous results for these problems and provide a proof of impossibility of a polynomialtime approximation scheme for the interior and boundary cover problems. The second problem concerns routing in a segmented routing channel. The related problems are fundamental to routing and design automation for Field Programmable Gate Arrays (FPGAs), a new type of electrically programmable VLSI. In ...