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Geometric Range Searching and Its Relatives
 CONTEMPORARY MATHEMATICS
"... ... process a set S of points in so that the points of S lying inside a query R region can be reported or counted quickly. Wesurvey the known techniques and data structures for range searching and describe their application to other related searching problems. ..."
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Cited by 257 (41 self)
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... process a set S of points in so that the points of S lying inside a query R region can be reported or counted quickly. Wesurvey the known techniques and data structures for range searching and describe their application to other related searching problems.
Making data structures persistent
, 1989
"... This paper is a study of persistence in data structures. Ordinary data structures are ephemeral in the sense that a change to the structure destroys the old version, leaving only the new version available for use. In contrast, a persistent structure allows access to any version, old or new, at any t ..."
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Cited by 256 (5 self)
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This paper is a study of persistence in data structures. Ordinary data structures are ephemeral in the sense that a change to the structure destroys the old version, leaving only the new version available for use. In contrast, a persistent structure allows access to any version, old or new, at any time. We develop simple, systematic, and efftcient techniques for making linked data structures persistent. We use our techniques to devise persistent forms of binary search trees with logarithmic access, insertion, and deletion times and O (1) space bounds for insertion and deletion.
A functional approach to data structures and its use in multidimensional searching
 SIAM J. Comput
, 1988
"... Abstract. We establish new upperbounds on the complexity ofmultidimensional 3earching. Our results include, in particular, linearsize data structures for range and rectangle counting in two dimensions with logarithmic query time. More generally, we give improved data structures for rectangle proble ..."
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Cited by 133 (3 self)
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Abstract. We establish new upperbounds on the complexity ofmultidimensional 3earching. Our results include, in particular, linearsize data structures for range and rectangle counting in two dimensions with logarithmic query time. More generally, we give improved data structures for rectangle problems in any dimension, in a static as well as a dynamic setting. Several ofthe algorithms we give are simple to implement and might be the solutions of choice in practice. Central to this paper is the nonstandard approach followed to achieve these results. At its rootwe find a redefinition ofdata structures interms offunctional specifications.
Tradeoffs for Packet Classification
"... We present an algorithmic framework for solving the packet classification problem that allows various access time vs. memory tradeoffs. It reduces the multidimensional packet classification problem to solving a few instances of the onedimensional IP lookup problem. It gives the best known lookup ..."
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Cited by 112 (1 self)
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We present an algorithmic framework for solving the packet classification problem that allows various access time vs. memory tradeoffs. It reduces the multidimensional packet classification problem to solving a few instances of the onedimensional IP lookup problem. It gives the best known lookup performance with moderately large memory space. Furthermore, it efficiently supports a reasonable number of additions and deletions to the rulesets without degrading the lookup performance. We perform a thorough experimental study of the tradeoffs for the twodimensional packet classification problem on rulesets derived from datasets collected from AT&T WorldNet, an Internet Service Provider.
External Memory Data Structures
, 2001
"... In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynami ..."
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Cited by 83 (37 self)
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In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used in practice.
On TwoDimensional Indexability and Optimal Range Search Indexing (Extended Abstract)
, 1999
"... Lars Arge Vasilis Samoladas y Jeffrey Scott Vitter z Abstract In this paper we settle several longstanding open problems in theory of indexability and external orthogonal range searching. In the first part of the paper, we apply the theory of indexability to the problem of twodimensional rang ..."
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Cited by 81 (28 self)
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Lars Arge Vasilis Samoladas y Jeffrey Scott Vitter z Abstract In this paper we settle several longstanding open problems in theory of indexability and external orthogonal range searching. In the first part of the paper, we apply the theory of indexability to the problem of twodimensional range searching. We show that the special case of 3sided querying can be solved with constant redundancy and access overhead. From this, we derive indexing schemes for general 4sided range queries that exhibit an optimal tradeoff between redundancy and access overhead.
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 71 (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.
An optimal algorithm for finding segments intersections
 In Proc. 11th Sympos. on Comput. Geom
, 1995
"... This paper deals with a new deterministic algorithm for finding intersecting pairs from a given set of N segments in the plane. The algorithm is asymptotically optimal and has time and space complexity O(AJ log N+ K) and 0 ( IV) respectively, where K is the number of intersecting pairs. The algorit ..."
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Cited by 69 (0 self)
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This paper deals with a new deterministic algorithm for finding intersecting pairs from a given set of N segments in the plane. The algorithm is asymptotically optimal and has time and space complexity O(AJ log N+ K) and 0 ( IV) respectively, where K is the number of intersecting pairs. The algorithm may be used for finding intersections not only line segments but also curve segments.
New data structures for orthogonal range searching
 In Proc. 41st IEEE Symposium on Foundations of Computer Science
, 2000
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Lower bounds for orthogonal range searching: I. the reporting case
 Journal of the ACM
, 1990
"... Abstract. We establish lower bounds on the complexity of orthogonal range reporting in the static case. Given a collection of n points in dspace and a box [a,, b,] x. x [ad, bd], report every point whose ith coordinate lies in [a,, biJ, for each i = 1,..., d. The collection of points is fixed once ..."
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Cited by 65 (4 self)
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Abstract. We establish lower bounds on the complexity of orthogonal range reporting in the static case. Given a collection of n points in dspace and a box [a,, b,] x. x [ad, bd], report every point whose ith coordinate lies in [a,, biJ, for each i = 1,..., d. The collection of points is fixed once and for all and can be preprocessed. The box, on the other hand, constitutes a query that must be answered online. It is shown that on a pointer machine a query time of O(k + polylog(n)), where k is the number of points to be reported, can only be achieved at the expense of fl(n(logn/loglogn)d‘) storage. Interestingly, these bounds are optimal in the pointer machine model, but they can be improved (ever so slightly) on a random access machine. In a companion paper, we address the related problem of adding up weights assigned to the points in the query box.