Results 1  10
of
16
A Subexponential Bound for Linear Programming
 ALGORITHMICA
, 1996
"... We present a simple randomized algorithm which solves linear programs with n constraints and d variables in expected min{O(d 2 2 d n),e 2 d ln(n / d)+O ( d+ln n)} time in the unit cost model (where we count the number of arithmetic operations on the numbers in the input); to be precise, the algorith ..."
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Cited by 167 (16 self)
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We present a simple randomized algorithm which solves linear programs with n constraints and d variables in expected min{O(d 2 2 d n),e 2 d ln(n / d)+O ( d+ln n)} time in the unit cost model (where we count the number of arithmetic operations on the numbers in the input); to be precise, the algorithm computes the lexicographically smallest nonnegative point satisfying n given linear inequalities in d variables. The expectation is over the internal randomizations performed by the algorithm, and holds for any input. In conjunction with Clarkson’s linear programming algorithm, this gives an expected bound of O(d 2 n + e O( √ d ln d) The algorithm is presented in an abstract framework, which facilitates its application to several other related problems like computing the smallest enclosing ball (smallest volume enclosing ellipsoid) of n points in dspace, computing the distance of two nvertex (or nfacet) polytopes in dspace, and others. The subexponential running time can also be established for some of these problems (this relies on some recent results due to Gärtner).
Query indexing and velocity constrained indexing: Scalable techniques for continuous queries on moving objects
 IEEE Transaction Computers
, 2002
"... Moving object environments are characterized by large numbers of moving objects and numerous concurrent continuous queries over these objects. Efficient evaluation of these queries in response to the movement of the objects is critical for supporting acceptable response times. In such environments t ..."
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Cited by 119 (19 self)
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Moving object environments are characterized by large numbers of moving objects and numerous concurrent continuous queries over these objects. Efficient evaluation of these queries in response to the movement of the objects is critical for supporting acceptable response times. In such environments the traditional approach of building an index on the objects (data) suffers from the need for frequent updates and thereby results in poor performance. In fact, a brute force, noindex strategy yields better performance in many cases. Neither the traditional approach, nor the brute force strategy achieve reasonable query processing times. This paper develops novel techniques for the efficient and scalable evaluation of multiple continuous queries on moving objects. Our solution leverages two complimentary techniques: Query Indexing and Velocity Constrained Indexing (VCI). Query Indexing relies on i) incremental evaluation; ii) reversing the role of queries and data; and iii) exploiting the relative locations of objects and queries. VCI takes advantage of the maximum possible speed of objects in order to delay the expensive operation of updating an index to reflect the movement of objects. In contrast to an earlier technique [29] that requires exact knowledge about the movement of the objects, VCI does not rely on such information. While Query Indexing outperforms VCI, it does not efficiently handle the arrival of new queries. Velocity constrained indexing, on the other hand, is unaffected by changes in queries. We demonstrate that a combination of Query Indexing and Velocity Constrained Indexing enables the scalable execution of insertion and deletion of queries in addition
Efficient algorithms for geometric optimization
 ACM Comput. Surv
, 1998
"... We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear progra ..."
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Cited by 94 (12 self)
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We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear programming and related problems, and LPtype problems and their efficient solution. We then describe a variety of applications of these and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other querytype problems.
Recognition Using Region Correspondences
 International Journal of Computer Vision
, 1995
"... A central problem in object recognition is to determine the transformation that relates the model to the image, given some partial correspondence between the two. This is useful in determining whether an object is present in an image, and if so, determining where the object is. We present a novel me ..."
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Cited by 34 (7 self)
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A central problem in object recognition is to determine the transformation that relates the model to the image, given some partial correspondence between the two. This is useful in determining whether an object is present in an image, and if so, determining where the object is. We present a novel method of solving this problem that uses region information. In our approach the model is divided into volumes, and the image is divided into regions. Given a match between subsets of volumes and regions (without any explicit correspondence between different pieces of the regions) the alignment transformation is computed. The method applies to planar objects under similarity, affine, and projective transformations and to projections of 3D objects undergoing affine and projective transformations. 1 Introduction A fundamental problem in recognition is pose estimation. Given a correspondence between some portions of an object model and some portions of an image, determine the transformation th...
Rectilinear and Polygonal pPiercing and pCenter Problems
 In Proc. 12th Annu. ACM Sympos. Comput. Geom
, 1996
"... We consider the ppiercing problem, in which we are given a collection of regions, and wish to determine whether there exists a set of p points that intersects each of the given regions. We give linear or nearlinear algorithms for small values of p in cases where the given regions are either axispa ..."
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Cited by 30 (1 self)
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We consider the ppiercing problem, in which we are given a collection of regions, and wish to determine whether there exists a set of p points that intersects each of the given regions. We give linear or nearlinear algorithms for small values of p in cases where the given regions are either axisparallel rectangles or convex coriented polygons in the plane (i.e., convex polygons with sides from a fixed finite set of directions) . We also investigate the planar rectilinear (and polygonal) pcenter problem, in which we are given a set S of n points in the plane, and wish to find p axisparallel congruent squares (isothetic copies of some given convex polygon, respectively) of smallest possible size whose union covers S. We also study several generalizations of these problems. New results are a lineartime solution for the rectilinear 3center problem (by showing that this problem can be formulated as an LPtype problem and by exhibiting a relation to Helly numbers). We give O(n log n...
Linear programming  randomization and abstract frameworks
 In Proc. 13th annu. Symp. on Theoretical Aspects of Computer Science (STACS
, 1996
"... Recent years have brought some progress in the knowledge of the complexity of linear programming in the unit cost model, and the best result known at this point is a randomized ‘combinatorial ’ algorithm which solves a linear program over d variables and n constraints with expected O(d 2 n + e O( d ..."
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Cited by 24 (9 self)
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Recent years have brought some progress in the knowledge of the complexity of linear programming in the unit cost model, and the best result known at this point is a randomized ‘combinatorial ’ algorithm which solves a linear program over d variables and n constraints with expected O(d 2 n + e O( d log d)) arithmetic operations. The bound relies on two algorithms by Clarkson, and the subexponential algorithms due to Kalai, and to Matouˇsek, Sharir & Welzl. frameworks like LPtype problems and abstract optimization problems (due to Gärtner) which allow the application of these algorithms to a number of nonlinear optimization problems (like polytope distance and smallest enclosing ball of points).
Randomized algorithms for geometric optimization problems
 Handbook of Randomized Computation
, 2001
"... This chapter reviews randomization algorithms developed in the last few years to solve a wide range of geometric optimization problems. We rst review a number of general techniques, including randomized binary search, randomized linearprogramming algorithms, and random sampling. Next, we describe s ..."
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Cited by 9 (0 self)
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This chapter reviews randomization algorithms developed in the last few years to solve a wide range of geometric optimization problems. We rst review a number of general techniques, including randomized binary search, randomized linearprogramming algorithms, and random sampling. Next, we describe several applications of these and other techniques, including facility location, proximity problems, statistical estimators, nearest neighbor searching, and Euclidean TSP.
Violator spaces: Structure and algorithms
 IN PROC. 14TH ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA
, 2006
"... Sharir and Welzl introduced an abstract framework for optimization problems, called LPtype problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a p ..."
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Cited by 8 (1 self)
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Sharir and Welzl introduced an abstract framework for optimization problems, called LPtype problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LPtype problems. We show that Clarkson’s randomized algorithms for lowdimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the Pmatrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LPtype problems: they are equivalent to acyclic violator spaces, as well as to concrete LPtype problems (informally, the constraints in a concrete LPtype problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).
3D to 2D Pose Determination with Regions
 International Journal of Computer Vision
, 1999
"... This paper presents a novel approach to partsbased object recognition in the presence of occlusion. We focus on the problem of determining the pose of a 3D object from a single 2D image when convex parts of the object have been matched to corresponding regions in the image. We consider three t ..."
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Cited by 7 (0 self)
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This paper presents a novel approach to partsbased object recognition in the presence of occlusion. We focus on the problem of determining the pose of a 3D object from a single 2D image when convex parts of the object have been matched to corresponding regions in the image. We consider three types of occlusions: selfocclusion, occlusions whose locus is identified in the image, and completely arbitrary occlusions. We show that in the first two cases this is a convex optimization problem, derive efficient algorithms, and characterize their performance. For the last case, we prove that the problem of finding valid poses is computationally hard, but provide an efficient, approximate algorithm. This work generalizes our previous work on regionbased object recognition, which focused on the case of planar models. This research was supported by the Unites StatesIsrael Binational Science Foundation, Grant No. 94100. The vision group at the Weizmann Inst. is supported in part by...
Conservative Visibility Preprocessing for Walkthroughs of Complex Urban Scenes
 In Proceedings of the ACM Symposium on Virtual Reality Software and Technology
, 2000
"... Visibility preprocessing is a useful method to reduce the complexity of scenes to be processed in realtime, and so enhances the overall rendering performance for interactive visualization of virtual environments. In this paper, we propose an efficient visibility preprocessing method. The proposed m ..."
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Cited by 5 (0 self)
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Visibility preprocessing is a useful method to reduce the complexity of scenes to be processed in realtime, and so enhances the overall rendering performance for interactive visualization of virtual environments. In this paper, we propose an efficient visibility preprocessing method. The proposed method is able to handle more general environments, like urban environments , and remove invisible polygons jointly blocked by multiple occluders. The proposed method requires O(nm) time and O(n+m) space. By selecting a suitable value for m, user can select a suitable level of tradeoff between the preprocessing time and the quality of the computational result. In the proposed method, we assume that navigatable areas in virtual environments are partitioned into rectangular parallelepiped cells or subworlds. To preprocess the visibility of each polygon for a given partitioned cell, we should determine at least the areatoarea visibility. That is inherently a fourdimensional problem. In the proposed method, we efficiently express fourdimensional visibility information on twodimensional spaces and keep it within a ternary tree, which is conceptually similar to a BSP(Binary Space Partitioning) tree, by exploiting the characteristics of conservative visibility.