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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 250 (39 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.
Indexing for data models with constraints and classes
 Journal of Computer and System Sciences
, 1996
"... We examine I Oefficient data structures that provide indexing support for new data models. The database languages of these models include concepts from constraint programming (e.g., relational tuples are generated to conjunctions of constraints) and from objectoriented programming (e.g., objects a ..."
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Cited by 113 (20 self)
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We examine I Oefficient data structures that provide indexing support for new data models. The database languages of these models include concepts from constraint programming (e.g., relational tuples are generated to conjunctions of constraints) and from objectoriented programming (e.g., objects are organized in class hierarchies). Let n be the size of the database, c the number of classes, B the page size on secondary storage, and t the size of the output of a query: (1) Indexing by one attribute in many constraint data models is equivalent to external dynamic interval management, which is a special case of external dynamic twodimensional range searching. We present a semidynamic data structure for this problem that has worstcase space O(n B) pages, query I O time O(logB n+t B) and O(logB n+(logB n) 2 B) amortized insert I O time. Note that, for the static version of this problem, this is the first worstcase optimal solution. (2) Indexing by one attribute and by class name in an objectoriented model, where objects are organized
Fast and Scalable Layer Four Switching
, 1998
"... In Layer Four switching, the route and resources allocated to a packet are determined by the destination address as well as other header fields of the packet such as source address, TCP and UDP port numbers. Layer Four switching unifies firewall processing, RSVP style resource reservation filters, Q ..."
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Cited by 111 (7 self)
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In Layer Four switching, the route and resources allocated to a packet are determined by the destination address as well as other header fields of the packet such as source address, TCP and UDP port numbers. Layer Four switching unifies firewall processing, RSVP style resource reservation filters, QoS Routing, and normal unicast and multicast forwarding into a single framework. In this framework, the forwarding database of a router consists of a potentially large number of filters on key header fields. A given packet header can match multiple filters, so each filter is given a cost, and the packet is forwarded using the least cost matching filter. In this paper, we describe two new algorithms for solving the least cost matching filter problem at high speeds. Our first algorithm is based on a gridoftries construction and works optimally for processing filters consisting of two prefix fields (such as destinationsource filters) using linear space. Our second algorithm, crossproducting, provides fast lookup times for arbitrary filters but potentially requires large storage. We describe a combination scheme that combines the advantages of both schemes. The combination scheme can be optimized to handle pure destination prefix filters in 4 memory accesses, destinationsource filters in 8 memory accesses worst case, and all other filters in 11 memory accesses in the typical case.
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 79 (36 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.
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.
New data structures for orthogonal range searching
 In Proc. 41st IEEE Symposium on Foundations of Computer Science
, 2000
"... ..."
Geometric Range Searching
, 1994
"... In geometric range searching, algorithmic problems of the following type are considered: Given an npoint set P in the plane, build a data structure so that, given a query triangle R, the number of points of P lying in R can be determined quickly. Problems of this type are of crucial importance in c ..."
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Cited by 46 (2 self)
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In geometric range searching, algorithmic problems of the following type are considered: Given an npoint set P in the plane, build a data structure so that, given a query triangle R, the number of points of P lying in R can be determined quickly. Problems of this type are of crucial importance in computational geometry, as they can be used as subroutines in many seemingly unrelated algorithms. We present a survey of results and main techniques in this area.
Optimal Dynamic Range Searching in Nonreplicating Index Structures
 In Proc. International Conference on Database Theory, LNCS 1540
, 1997
"... We consider the problem of dynamic range searching in tree structures that do not replicate data. We propose a new dynamic structure, called the Otree, that achieves a query time complexity of O(n (d\Gamma1)=d ) on n ddimensional points and an amortized insertion/deletion time complexity of O(l ..."
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Cited by 26 (2 self)
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We consider the problem of dynamic range searching in tree structures that do not replicate data. We propose a new dynamic structure, called the Otree, that achieves a query time complexity of O(n (d\Gamma1)=d ) on n ddimensional points and an amortized insertion/deletion time complexity of O(log n). We show that this structure is optimal when data is not replicated. In addition to optimal query and insertion/deletion times, the Otree also supports exact match queries in worstcase logarithmic time. 1 Introduction Given a set S of ddimensional points, a range query q is specified by d 1dimensional intervals [q s i ; q e i ], one for each dimension i, and retrieves all points p = (p 1 ; p 2 ; : : : p d ) in S such that h8i 2 f1; : : : ; dg : q s i p i q e i i. This type of searching in multidimensional space has important applications in geographic information systems, image databases, and computer graphics. Several structures such as the range trees [3], Prange trees [29...
Cacheoblivious data structures for orthogonal range searching
 IN PROC. ACM SYMPOSIUM ON COMPUTATIONAL GEOMETRY
, 2003
"... We develop cacheoblivious data structures for orthogonal range searching, the problem of finding all T points in a set of N points in Rd lying in a query hyperrectangle. Cacheoblivious data structures are designed to be efficient in arbitrary memory hierarchies. We describe a dynamic linearsize ..."
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Cited by 22 (6 self)
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We develop cacheoblivious data structures for orthogonal range searching, the problem of finding all T points in a set of N points in Rd lying in a query hyperrectangle. Cacheoblivious data structures are designed to be efficient in arbitrary memory hierarchies. We describe a dynamic linearsize data structure that answers ddimensional queries in O((N/B)11/d + T/B) memory transfers, where B is the block size of any two levels of a multilevel memory hierarchy. A point can be inserted into or deleted from this data structure in O(log2B N) memory transfers. We also develop a static structure for the twodimensional case that answers queries in O(logB N + T /B) memory transfers using O(N log22 N) space. The analysis of the latter structure requires that B = 22 c for some nonnegative integer constant c.
How Hard Is Halfspace Range Searching?
, 1993
"... We investigate the complexity of halfspace range searching: Given n points in d space, build a data structure that allows us to determine efficiently how many points lie in a query halfspace. We establish a tradeoff between the storage m and the worstcase query time t in the Fredman/Yao arithmetic ..."
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Cited by 20 (0 self)
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We investigate the complexity of halfspace range searching: Given n points in d space, build a data structure that allows us to determine efficiently how many points lie in a query halfspace. We establish a tradeoff between the storage m and the worstcase query time t in the Fredman/Yao arithmetic model of computation. We show that t must be at least on the order of (n= log n) 1\Gamma d\Gamma1 d(d+1) =m 1=d : Although the bound is unlikely to be optimal, it falls reasonably close to the recent upper bound of O \Gamma n=m 1=d \Delta upper bound established by Matousek. We also show that it is possible to devise a sequence of n inserts and halfspace range queries that require a total time of n 2\GammaO(1=d) . Our results imply the first nontrivial lower bounds for spherical range searching in any fixed dimension. For example they show that, with linear storage, circular range queries in the plane require\Omega \Gamma n 1=3 \Delta time (modulo a logarithmic factor).