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86
Range Searching
, 1996
"... Range searching is one of the central problems in computational geometry, because it arises in many applications and a wide variety of geometric problems can be formulated as a rangesearching problem. A typical rangesearching problem has the following form. Let S be a set of n points in R d , an ..."
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Cited by 70 (1 self)
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Range searching is one of the central problems in computational geometry, because it arises in many applications and a wide variety of geometric problems can be formulated as a rangesearching problem. A typical rangesearching problem has the following form. Let S be a set of n points in R d , and let R be a family of subsets; elements of R are called ranges . We wish to preprocess S into a data structure so that for a query range R, the points in S " R can be reported or counted efficiently. Typical examples of ranges include rectangles, halfspaces, simplices, and balls. If we are only interested in answering a single query, it can be done in linear time, using linear space, by simply checking for each point p 2 S whether p lies in the query range.
Geometric approximation via coresets
 Combinatorial and Computational Geometry, MSRI
, 2005
"... Abstract. The paradigm of coresets has recently emerged as a powerful tool for efficiently approximating various extent measures of a point set P. Using this paradigm, one quickly computes a small subset Q of P, called a coreset, that approximates the original set P and and then solves the problem o ..."
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Cited by 60 (7 self)
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Abstract. The paradigm of coresets has recently emerged as a powerful tool for efficiently approximating various extent measures of a point set P. Using this paradigm, one quickly computes a small subset Q of P, called a coreset, that approximates the original set P and and then solves the problem on Q using a relatively inefficient algorithm. The solution for Q is then translated to an approximate solution to the original point set P. This paper describes the ways in which this paradigm has been successfully applied to various optimization and extent measure problems. 1.
The Priority RTree: A Practically Efficient and WorstCase Optimal RTree
 SIGMOD 2004 JUNE 1318, 2004, PARIS, FRANCE
, 2004
"... We present the Priority Rtree, or PRtree, which is the first Rtree variant that always answers a window query using O((N/B) 1−1/d + T/B) I/Os, where N is the number of ddimensional (hyper) rectangles stored in the Rtree, B is the disk block size, and T is the output size. This is provably asymp ..."
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Cited by 56 (7 self)
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We present the Priority Rtree, or PRtree, which is the first Rtree variant that always answers a window query using O((N/B) 1−1/d + T/B) I/Os, where N is the number of ddimensional (hyper) rectangles stored in the Rtree, B is the disk block size, and T is the output size. This is provably asymptotically optimal and significantly better than other Rtree variants, where a query may visit all N/B leaves in the tree even when T = 0. We also present an extensive experimental study of the practical performance of the PRtree using both reallife and synthetic data. This study shows that the PRtree performs similar to the best known Rtree variants on reallife and relatively nicely distributed data, but outperforms them significantly on more extreme data.
Optimal Bounds for the Predecessor Problem and Related Problems
 Journal of Computer and System Sciences
, 2001
"... We obtain matching upper and lower bounds for the amount of time to find the predecessor of a given element among the elements of a fixed compactly stored set. Our algorithms are for the unitcost word RAM with multiplication and are extended to give dynamic algorithms. The lower bounds are proved ..."
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Cited by 55 (0 self)
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We obtain matching upper and lower bounds for the amount of time to find the predecessor of a given element among the elements of a fixed compactly stored set. Our algorithms are for the unitcost word RAM with multiplication and are extended to give dynamic algorithms. The lower bounds are proved for a large class of problems, including both static and dynamic predecessor problems, in a much stronger communication game model, but they apply to the cell probe and RAM models.
The multiplicative weights update method: a meta algorithm and applications
, 2005
"... Algorithms in varied fields use the idea of maintaining a distribution over a certain set and use the multiplicative update rule to iteratively change these weights. Their analysis are usually very similar and rely on an exponential potential function. We present a simple meta algorithm that unifies ..."
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Cited by 53 (10 self)
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Algorithms in varied fields use the idea of maintaining a distribution over a certain set and use the multiplicative update rule to iteratively change these weights. Their analysis are usually very similar and rely on an exponential potential function. We present a simple meta algorithm that unifies these disparate algorithms and drives them as simple instantiations of the meta algorithm. 1
A transport layer approach for improving endtoend performance and robustness using redundant paths
 In USENIX Annual Technical Conference
, 2004
"... Recent work on Internet measurement and overlay networks has shown that redundant paths are common between pairs of hosts and that one can often achieve better endtoend performance by adaptively choosing an alternate path [8, 27]. In this paper, we propose an endtoend transport layer protocol, m ..."
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Cited by 52 (3 self)
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Recent work on Internet measurement and overlay networks has shown that redundant paths are common between pairs of hosts and that one can often achieve better endtoend performance by adaptively choosing an alternate path [8, 27]. In this paper, we propose an endtoend transport layer protocol, mTCP, which can aggregate the available bandwidth of those redundant paths in parallel. By striping one flow’s packets across multiple paths, mTCP can not only obtain higher endtoend throughput but also be more robust under path failures. When some paths fail, mTCP can continue sending packets on other paths, and the recovery process normally takes only a few seconds. Because mTCP could obtain an unfair share of bandwidth under shared congestion, we integrate a shared congestion detection mechanism into our system. It allows us to dynamically detect and suppress paths with shared congestion so as to alleviate the aggressiveness problem. mTCP can also passively monitor the performance of several paths in parallel and discover better paths than the path provided by the underlying routing infrastructure. We also propose a heuristic to find disjoint paths between pairs of nodes using traceroute. We have implemented our system on top of overlay networks and evaluated it in both PlanetLab and Emulab. 1
Approximating the Minimum Spanning Tree Weight in Sublinear Time
 In Proceedings of the 28th Annual International Colloquium on Automata, Languages and Programming (ICALP
, 2001
"... We present a probabilistic algorithm that, given a connected graph G (represented by adjacency lists) of average degree d, with edge weights in the set {1,...,w}, and given a parameter 0 < ε < 1/2, estimates in time O(dwε−2 log dw ε) the weight of the minimum spanning tree of G with a relative erro ..."
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Cited by 38 (6 self)
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We present a probabilistic algorithm that, given a connected graph G (represented by adjacency lists) of average degree d, with edge weights in the set {1,...,w}, and given a parameter 0 < ε < 1/2, estimates in time O(dwε−2 log dw ε) the weight of the minimum spanning tree of G with a relative error of at most ε. Note that the running time does not depend on the number of vertices in G. We also prove a nearly matching lower bound of Ω(dwε−2) on the probe and time complexity of any approximation algorithm for MST weight. The essential component of our algorithm is a procedure for estimating in time O(dε−2 log d ε) the number of connected components of an unweighted graph to within an additive error of εn. (This becomes O(ε−2 log 1 ε) for d = O(1).) The time bound is shown to be tight up to within the log d ε factor. Our connectedcomponents algorithm picks O(1/ε2) vertices in the graph and then grows “local spanning trees” whose sizes are specified by a stochastic process. From the local information collected in this way, the algorithm is able to infer, with high confidence, an estimate of the number of connected components. We then show how estimates on the number of components in various subgraphs of G can be used to estimate the weight of its MST. 1
Domain Adaptation: Learning Bounds and Algorithms
"... This paper addresses the general problem of domain adaptation which arises in a variety of applications where the distribution of the labeled sample available somewhat differs from that of the test data. Building on previous work by BenDavid et al. (2007), we introduce a novel distance between dist ..."
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Cited by 22 (4 self)
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This paper addresses the general problem of domain adaptation which arises in a variety of applications where the distribution of the labeled sample available somewhat differs from that of the test data. Building on previous work by BenDavid et al. (2007), we introduce a novel distance between distributions, discrepancy distance, that is tailored to adaptation problems with arbitrary loss functions. We give Rademacher complexity bounds for estimating the discrepancy distance from finite samples for different loss functions. Using this distance, we derive new generalization bounds for domain adaptation for a wide family of loss functions. We also present a series of novel adaptation bounds for large classes of regularizationbased algorithms, including support vector machines and kernel ridge regression based on the empirical discrepancy. This motivates our analysis of the problem of minimizing the empirical discrepancy for various loss functions for which we also give several algorithms. We report the results of preliminary experiments that demonstrate the benefits of our discrepancy minimization algorithms for domain adaptation. 1
Improved approximation algorithms for broadcast scheduling
 In Proc. of 7 th Annual ACMSIAM Symposium on Discrete Algorithms
, 2004
"... We consider two scheduling problems in the broadcast setting. The first is that of minimizing the average response time of requests. For the offline version of this problem we give an algorithm with an approximation ratio of O(log 2 (n) / log log(n)), where n is the total number of pages. This subst ..."
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Cited by 20 (0 self)
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We consider two scheduling problems in the broadcast setting. The first is that of minimizing the average response time of requests. For the offline version of this problem we give an algorithm with an approximation ratio of O(log 2 (n) / log log(n)), where n is the total number of pages. This substantially improves the previously best known approximation factor of O ( √ n) for the problem [3]. Our second result is for the profit maximization version of the broadcast scheduling problem. Here each request has a deadline and a profit which is obtained if the request is satisfied before its deadline. The goal is to maximize the total profit. We give an algorithm with an approximation ratio of 5/6, which improves the previously best known approximation guarantee of 3/4 for the problem [13]. 1
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 19 (2 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