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13
Sublinear geometric algorithms
 In Proc. of the 35th Annual ACM Symp. on Theory of Computing
, 2003
"... Abstract. We initiate an investigation of sublinear algorithms for geometric problems in two and three dimensions. We give optimal algorithms for intersection detection of convex polygons and polyhedra, point location in twodimensional triangulations and Voronoi diagrams, and ray shooting in convex ..."
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Cited by 24 (1 self)
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Abstract. We initiate an investigation of sublinear algorithms for geometric problems in two and three dimensions. We give optimal algorithms for intersection detection of convex polygons and polyhedra, point location in twodimensional triangulations and Voronoi diagrams, and ray shooting in convex polyhedra, all of which run in expected time O ( √ n), where n is the size of the input. We also provide sublinear solutions for the approximate evaluation of the volume of a convex polytope and the length of the shortest path between two points on the boundary. Key words. sublinear algorithms, approximate shortest paths, polyhedral intersection
Sublineartime algorithms
 In Oded Goldreich, editor, Property Testing, volume 6390 of Lecture Notes in Computer Science
, 2010
"... In this paper we survey recent (up to end of 2009) advances in the area of sublineartime algorithms. 1 ..."
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Cited by 19 (2 self)
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In this paper we survey recent (up to end of 2009) advances in the area of sublineartime algorithms. 1
Estimating the weight of metric minimum spanning trees in sublineartime
 in Proceedings of the 36th Annual ACM Symposium on Theory of Computing (STOC
"... In this paper we present a sublinear time (1+ ɛ)approximation randomized algorithm to estimate the weight of the minimum spanning tree of an npoint metric space. The running time of the algorithm is Õ(n/ɛO(1)). Since the full description of an npoint metric space is of size Θ(n 2),the complexity ..."
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Cited by 19 (5 self)
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In this paper we present a sublinear time (1+ ɛ)approximation randomized algorithm to estimate the weight of the minimum spanning tree of an npoint metric space. The running time of the algorithm is Õ(n/ɛO(1)). Since the full description of an npoint metric space is of size Θ(n 2),the complexity of our algorithm is sublinear with respect to the input size. Our algorithm is almost optimal as it is not possible to approximate in o(n) time the weight of the minimum spanning tree to within any factor. Furthermore,it has been previously shown that no o(n 2) algorithm exists that returns a spanning tree whose weight is within a constant times the optimum.
Abstract combinatorial programs and efficient property testers
, 2005
"... Property testing is a relaxation of classical decision problems which aims at distinguishing between functions having a predetermined property and functions being far from any function having the property. In this paper we present a novel framework for analyzing property testing algorithms. Our fr ..."
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Cited by 15 (6 self)
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Property testing is a relaxation of classical decision problems which aims at distinguishing between functions having a predetermined property and functions being far from any function having the property. In this paper we present a novel framework for analyzing property testing algorithms. Our framework is based on a connection of property testing and a new class of problems which we call abstract combinatorial programs. We show that if the problem of testing a property can be reduced to an abstract combinatorial program of small dimension, then the property has an efficient tester. We apply our framework to a variety of problems. We present efficient property testing algorithms for geometric clustering problems, for the reversal distance problem, and for graph and hypergraph coloring problems. We also prove that, informally, any hereditary graph property can be efficiently tested if and only if it can be reduced to an abstract combinatorial program of small size. Our framework allows us to analyze all our testers in a unified way, and the obtained complexity bounds either match or improve the previously known bounds. Furthermore, even if the asymptotic complexity of the testers is not improved, the obtained proofs are significantly simpler than the previous ones. We believe that our framework will help to understand the structure of efficiently testable properties.
Online geometric reconstruction
 Proc. of 22nd SOCG
, 2006
"... We investigate a new class of geometric problems based on the idea of online error correction. Suppose one is given access to a large geometric dataset though a query mechanism; for example, the dataset could be a terrain and a query might ask for the coordinates of a particular vertex or for the ed ..."
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Cited by 7 (2 self)
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We investigate a new class of geometric problems based on the idea of online error correction. Suppose one is given access to a large geometric dataset though a query mechanism; for example, the dataset could be a terrain and a query might ask for the coordinates of a particular vertex or for the edges incident to it. Suppose, in addition, that the dataset satisfies some known structural property P (eg, monotonicity or convexity) but that, because of errors and noise, the queries occasionally provide answers that violate P. Can one design a filter that modifies the query’s answers so that (i) the output satisfies P; (ii) the amount of data modification is minimized? We provide upper and lower bounds on the complexity of online reconstruction for convexity in 2D and 3D. 1
Hierarchical peertopeer networks using lightweight superpeer topologies
 Proc 10th IEEE Symposium on Computers and Communication (ICSS05), La Manga del Mar Menor
, 2005
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On derandomizing probabilistic sublineartime algorithms
 In Proceedings of the 22nd IEEE conference on computational complexity
, 2007
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Testing Euclidean minimum spanning trees in the plane
 ACM Transactions on Algorithms
, 2007
"... Given a Euclidean graph G over a set P of n points in the plane, we are interested in verifying whether G is a Euclidean minimum spanning tree (EMST) of P or G differs from it in more than ǫn edges. We assume that G is given in adjacency list representation and the point/vertex set P is given in an ..."
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Cited by 2 (2 self)
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Given a Euclidean graph G over a set P of n points in the plane, we are interested in verifying whether G is a Euclidean minimum spanning tree (EMST) of P or G differs from it in more than ǫn edges. We assume that G is given in adjacency list representation and the point/vertex set P is given in an array. We present a property testing algorithm that accepts graph G if it is an EMST of P and that rejects with probability at least 2 3 if G differs from every EMST of P in more than ǫn edges. Our algorithm runs in O ( � n/ǫ · log2 (n/ǫ)) time and has a query complexity of O ( � n/ǫ · log(n/ǫ)).
A case for lightweight superpeer topologies
 In KiVS Kurzbeiträge und Workshop
, 2005
"... Abstract: The usage of SuperPeers has been proposed to improve the performance of both Structured and Unstructured PeertoPeer (P2P) networks. In this paper we explore a networkaware class of Lightweight SuperPeer Topologies (LSTs). The proposed LST is based on the geometric principle of YaoGraph ..."
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Cited by 2 (1 self)
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Abstract: The usage of SuperPeers has been proposed to improve the performance of both Structured and Unstructured PeertoPeer (P2P) networks. In this paper we explore a networkaware class of Lightweight SuperPeer Topologies (LSTs). The proposed LST is based on the geometric principle of YaoGraphs, a class of graphs allowing the development of simple and efficient broadcast algorithms. The prerequisite of the LST approach is a function for mapping nodes in a network into a geometric space. In this paper we use the ”Highways ” proximity clustering and geometric placement model, introduced by one of the authors for this purpose. LST is evaluated based on PlanetLab measurements. 1