Results 11  20
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334
An optimal algorithm for intersecting line segments in the plane
 J. ACM
, 1992
"... Abstract. Themain contribution ofthiswork is an O(nlogr ~ +k)timeal gorithmfo rcomputingall k intersections among n line segments in the plane, This time complexity IS easdy shown to be optimal. Within thesame asymptotic cost, ouralgorithm canalso construct thesubdiwslon of theplancdefmed by the se ..."
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Cited by 161 (2 self)
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Abstract. Themain contribution ofthiswork is an O(nlogr ~ +k)timeal gorithmfo rcomputingall k intersections among n line segments in the plane, This time complexity IS easdy shown to be optimal. Within thesame asymptotic cost, ouralgorithm canalso construct thesubdiwslon of theplancdefmed by the segments and compute which segment (if any) lies right above (or below) each intersection and each endpoint. The algorithm has been implemented and performs very well. The storage requirement is on the order of n + k in the worst case, but it is considerably lower in practice. To analyze the complexity of the algorithm, an amortization argument based on a new combinatorial theorem on line arrangements is used.
Voronoi Diagrams
 Handbook of Computational Geometry
"... Voronoi diagrams can also be thought of as lower envelopes, in the sense mentioned at the beginning of this subsection. Namely, for each point x not situated on a bisecting curve, the relation p x q defines a total ordering on S. If we construct a set of surfaces H p , p S,in3space such t ..."
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Cited by 143 (19 self)
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Voronoi diagrams can also be thought of as lower envelopes, in the sense mentioned at the beginning of this subsection. Namely, for each point x not situated on a bisecting curve, the relation p x q defines a total ordering on S. If we construct a set of surfaces H p , p S,in3space such that H p is below H q i# p x q holds, then the projection of their lower envelope equals the abstract Voronoi diagram.
HighSpeed Policybased Packet Forwarding Using Efficient Multidimensional Range Matching
 In ACM SIGCOMM
, 1998
"... The ability to provide differentiated services to users with widely varying requirements is becoming increasingly important, and Internet Service Providers would like to provide these differentiated services using the same shared network infrastructure. The key mechanism, that enables differentiatio ..."
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Cited by 136 (0 self)
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The ability to provide differentiated services to users with widely varying requirements is becoming increasingly important, and Internet Service Providers would like to provide these differentiated services using the same shared network infrastructure. The key mechanism, that enables differentiation in a connectionless network, is the packet classification function that parses the headers of the packets, and after determining their context, classifies them based on administrative policies or realtime reservation decisions. Packet classification, however, is a complex operation that can become the bottleneck in routers that try to support gigabit link capacities. Hence, many proposals for differentiated services only require classification at lower speed edge routers and also avoid classification based on multiple fields in the packet header even if it might be advantageous to service providers. In this paper, we present new packet classification schemes that, with a worstcase and tr...
Efficient Indexing Methods for Probabilistic Threshold Queries over Uncertain Data
 Proc. 30th Int’l Conf. Very Large Data Bases (VLDB
, 2004
"... It is infeasible for a sensor database to contain the exact value of each sensor at all points in time. This uncertainty is inherent in these systems due to measurement and sampling errors, and resource limitations. In order to avoid drawing erroneous conclusions based upon stale data, the use of un ..."
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Cited by 105 (20 self)
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It is infeasible for a sensor database to contain the exact value of each sensor at all points in time. This uncertainty is inherent in these systems due to measurement and sampling errors, and resource limitations. In order to avoid drawing erroneous conclusions based upon stale data, the use of uncertainty intervals that model each data item as a range and associated probability density function (pdf) rather than a single value has recently been proposed. Querying these uncertain data introduces imprecision into answers, in the form of probability values that specify the likeliness the answer satisfies the query. These queries are more expensive to evaluate than their traditional counterparts but are guaranteed to be correct and more informative due to the probabilities accompanying the answers. Although the answer probabilities are useful, for many applications, it is only necessary to know whether the probability exceeds a given threshold – we term these Probabilistic Threshold Queries (PTQ). In this paper we address the efficient computation of these types of queries. In particular, we develop two index structures and associated algorithms to efficiently answer PTQs. The first index scheme is based on the idea of augmenting uncertainty information to an Rtree. We establish the difficulty
Las Vegas algorithms for linear and integer programming when the dimension is small
 J. ACM
, 1995
"... Abstract. This paper gives an algcmthm for solving linear programming problems. For a problem with tz constraints and d variables, the algorithm requires an expected O(d’n) + (log n)o(d)d’’+(’(’) + o(dJA log n) arithmetic operations, as rz ~ ~. The constant factors do not depend on d. Also, an algor ..."
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Cited by 103 (2 self)
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Abstract. This paper gives an algcmthm for solving linear programming problems. For a problem with tz constraints and d variables, the algorithm requires an expected O(d’n) + (log n)o(d)d’’+(’(’) + o(dJA log n) arithmetic operations, as rz ~ ~. The constant factors do not depend on d. Also, an algorlthm N gwen for integer hnear programmmg. Let p bound the number of bits required to specify the ratmnal numbers defmmg an input constraint or the ob~ective function vector. Let n and d be as before. Then, the algorithm requires expected 0(2d dn + S~dm In n) + dc)’d) ~ in H operations on numbers with O(1~p bits d ~ ~ ~z + ~, where the constant factors do not depend on d or p. The expectations are with respect to the random choices made by the algorithms, and the bounds hold for any gwen input. The techmque can be extended to other convex programming problems. For example, m algorlthm for finding the smallest sphere enclosing a set of /z points m Ed has the same t]me bound
Fast construction of nets in lowdimensional metrics and their applications
 SIAM Journal on Computing
, 2006
"... We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This datastructure is then applied to obtain improved algorithms for the following problems: approximate nearest neighbor search, wellseparated pair decomposition, s ..."
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Cited by 98 (10 self)
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We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This datastructure is then applied to obtain improved algorithms for the following problems: approximate nearest neighbor search, wellseparated pair decomposition, spanner construction, compact representation scheme, doubling measure, and computation of the (approximate) Lipschitz constant of a function. In all cases, the running (preprocessing) time is near linear and the space being used is linear. 1
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.
Four Results on Randomized Incremental Constructions
 Comput. Geom. Theory Appl
, 1993
"... We prove four results on randomized incremental constructions (RICs): ffl an analysis of the expected behavior under insertion and deletions, ffl a fully dynamic data structure for convex hull maintenance in arbitrary dimensions, ffl a tail estimate for the space complexity of RICs, ffl a lower ..."
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Cited by 92 (17 self)
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We prove four results on randomized incremental constructions (RICs): ffl an analysis of the expected behavior under insertion and deletions, ffl a fully dynamic data structure for convex hull maintenance in arbitrary dimensions, ffl a tail estimate for the space complexity of RICs, ffl a lower bound on the complexity of a game related to RICs. 1
Applications of parametric searching in geometric optimization
 J. Algorithms
, 1994
"... z Sivan Toledo x ..."