Results 11  20
of
72
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 ..."
Abstract

Cited by 74 (1 self)
 Add to MetaCart
(Show Context)
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.
Efficient Searching with Linear Constraints (Extended Abstract)
"... We show how to preprocess a set S of points in R d to get an external memory data structure that efficiently supports linearconstraint queries. Each query is in the form of a linear constraint a \Delta x b; the data structure must report all the points of S that satisfy the query. Our goal i ..."
Abstract

Cited by 58 (16 self)
 Add to MetaCart
We show how to preprocess a set S of points in R d to get an external memory data structure that efficiently supports linearconstraint queries. Each query is in the form of a linear constraint a \Delta x b; the data structure must report all the points of S that satisfy the query. Our goal is to minimize the number of disk blocks required to store the data structure and the number of disk accesses (I/Os) required to answer a query. For d = 2, we present the first nearlinear size data structures that can answer linearconstraint queries using an optimal number of I/Os. We also present a linearsize data structure that can answer queries efficiently in the worst case. We combine these two approaches to obtain tradeoffs between space and query time. Finally, we show that some of our techniques extend to higher dimensions d.
Optimal external memory interval management
 SIAM Journal on Computing
"... This work has been made available by the University of Kansas ..."
Abstract

Cited by 50 (7 self)
 Add to MetaCart
This work has been made available by the University of Kansas
Efficient External Memory Algorithms by Simulating CoarseGrained Parallel Algorithms
, 2003
"... External memory (EM) algorithms are designed for largescale computational problems in which the size of the internal memory of the computer is only a small fraction of the problem size. Typical EM algorithms are specially crafted for the EM situation. In the past, several attempts have been made to ..."
Abstract

Cited by 46 (11 self)
 Add to MetaCart
(Show Context)
External memory (EM) algorithms are designed for largescale computational problems in which the size of the internal memory of the computer is only a small fraction of the problem size. Typical EM algorithms are specially crafted for the EM situation. In the past, several attempts have been made to relate the large body of work on parallel algorithms to EM, but with limited success. The combination of EM computing, on multiple disks, with multiprocessor parallelism has been posted as a challenge by the ACMWorking Group on Storage I/O for LargeScale Computing.
Orthogonal Range Searching on the RAM, Revisited
, 2011
"... We present a number of new results on one of the most extensively studied topics in computational geometry, orthogonal range searching. All our results are in the standard word RAM model: 1. We present two data structures for 2d orthogonal range emptiness. The first achieves O(n lg lg n) space and ..."
Abstract

Cited by 38 (7 self)
 Add to MetaCart
We present a number of new results on one of the most extensively studied topics in computational geometry, orthogonal range searching. All our results are in the standard word RAM model: 1. We present two data structures for 2d orthogonal range emptiness. The first achieves O(n lg lg n) space and O(lg lg n) query time, assuming that the n given points are in rank space. This improves the previous results by Alstrup, Brodal, and Rauhe (FOCS’00), with O(n lg ε n) space and O(lg lg n) query time, or with O(n lg lg n) space and O(lg 2 lg n) query time. Our second data structure uses O(n) space and answers queries in O(lg ε n) time. The best previous O(n)space data structure, due to Nekrich (WADS’07), answers queries in O(lg n / lg lg n) time. 2. We give a data structure for 3d orthogonal range reporting with O(n lg 1+ε n) space and O(lg lg n+ k) query time for points in rank space, for any constant ε> 0. This improves the previous results by Afshani (ESA’08), Karpinski and Nekrich (COCOON’09), and Chan (SODA’11), with O(n lg 3 n) space and O(lg lg n + k) query time, or with O(n lg 1+ε n) space and O(lg 2 lg n + k) query time. Consequently, we obtain improved upper bounds for orthogonal range reporting in all constant dimensions above 3.
Efficient ExternalMemory Data Structures and Applications
, 1996
"... In this thesis we study the Input/Output (I/O) complexity of largescale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer graphics, and design I/Oefficient algorithms for them. A general theme in our work is to design I/Oeffic ..."
Abstract

Cited by 38 (9 self)
 Add to MetaCart
(Show Context)
In this thesis we study the Input/Output (I/O) complexity of largescale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer graphics, and design I/Oefficient algorithms for them. A general theme in our work is to design I/Oefficient algorithms through the design of I/Oefficient data structures. One of our philosophies is to try to isolate all the I/O specific parts of an algorithm in the data structures, that is, to try to design I/O algorithms from internal memory algorithms by exchanging the data structures used in internal memory with their external memory counterparts. The results in the thesis include a technique for transforming an internal memory tree data structure into an external data structure which can be used in a batched dynamic setting, that is, a setting where we for example do not require that the result of a search operation is returned immediately. Using this technique we develop batched dynamic external versions of the (onedimensional) rangetree and the segmenttree and we develop an external priority queue. Following our general philosophy we show how these structures can be used in standard internal memory sorting algorithms
Geometric burrowswheeler transform: Linking range searching and text indexing
 In DCC
"... We introduce a new variant of the popular BurrowsWheeler transform (BWT) called Geometric BurrowsWheeler Transform (GBWT). Unlike BWT, which merely permutes the text, GBWT converts the text into a set of points in 2dimensional geometry. Using this transform, we can answer to many open questions i ..."
Abstract

Cited by 34 (3 self)
 Add to MetaCart
(Show Context)
We introduce a new variant of the popular BurrowsWheeler transform (BWT) called Geometric BurrowsWheeler Transform (GBWT). Unlike BWT, which merely permutes the text, GBWT converts the text into a set of points in 2dimensional geometry. Using this transform, we can answer to many open questions in compressed text indexing: (1) Can compressed data structures be designed in external memory with similar performance as the uncompressed counterparts? (2) Can compressed data structures be designed for position restricted pattern matching [16]? We also introduce a reverse transform, called Points2Text, which converts a set of points into text. This transform allows us to derive the first known lower bounds in compressed text indexing. We show strong equivalence between data structural problems in geometric range searching and text pattern matching. This provides a way to derive new results in compressed text indexing by translating the results from range searching. 1
Efficient 3D Range Searching in External Memory
 In Proc. ACM Symp. on Theory of Computation
, 1995
"... We present a new approach to designing data structures for the important problem of externalmemory range searching in two and three dimensions. We construct data structures for answering range queries in O((log log log B N) log B N + K=B) I/O operations, where N is the number of points in the data s ..."
Abstract

Cited by 30 (2 self)
 Add to MetaCart
(Show Context)
We present a new approach to designing data structures for the important problem of externalmemory range searching in two and three dimensions. We construct data structures for answering range queries in O((log log log B N) log B N + K=B) I/O operations, where N is the number of points in the data structure, B is the I/O block size, and K is the number of points in the answer to the query. Our data structures answer a longstanding open problem by providing three dimensional results comparable to those provided by [8, 10] for the two dimensional case, though completely new techniques are used. Ours is the first 3D range search data structure that simultaneously achieves both a baseB logarithmic search overhead (namely, (log log log B N) log B N) and a fully blocked output component (namely, K=B). This gives us an overall I/O complexity extremely close to the wellknown lower bound of \Omega\Gamma/89 B N +K=B). We base our data structures on the novel concept of Bapproximate boundarie...
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 ..."
Abstract

Cited by 30 (2 self)
 Add to MetaCart
(Show Context)
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...
Efficient Indexing for Constraint and Temporal Databases
 Proc. 6th Int. Conf. on Database Theory (ICDT), LNCS 1186
, 1997
"... . We examine new I/Oefficient techniques for indexing problems in constraint and temporal data models. We present algorithms for these problems that are considerably simpler than previous solutions. Our solutions are unique in the sense that they only use B + trees rather than specialpurpos ..."
Abstract

Cited by 29 (0 self)
 Add to MetaCart
(Show Context)
. We examine new I/Oefficient techniques for indexing problems in constraint and temporal data models. We present algorithms for these problems that are considerably simpler than previous solutions. Our solutions are unique in the sense that they only use B + trees rather than specialpurpose data structures. Indexing for many general constraint data models can be reduced to interval intersection. We present a new algorithm for this problem using a querytime/space tradeoff, which achieves the optimal query time O(log B n + t=B) I/O's in linear space O(n=B) using B + trees. (Here, n is the number of intervals, t the number of intervals in the output of a query, and B the disk block size.) It is easy to update this data structure, but small worstcase bounds do not seem possible. Previous approaches have achieved these bounds but are fairly complex and rely mostly on reducing the interval intersection problem to special cases of twodimensional search. Some of them c...