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The String BTree: A New Data Structure for String Search in External Memory and its Applications.
 Journal of the ACM
, 1998
"... We introduce a new textindexing data structure, the String BTree, that can be seen as a link between some traditional externalmemory and stringmatching data structures. In a short phrase, it is a combination of Btrees and Patricia tries for internalnode indices that is made more effective by a ..."
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Cited by 121 (11 self)
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We introduce a new textindexing data structure, the String BTree, that can be seen as a link between some traditional externalmemory and stringmatching data structures. In a short phrase, it is a combination of Btrees and Patricia tries for internalnode indices that is made more effective by adding extra pointers to speed up search and update operations. Consequently, the String BTree overcomes the theoretical limitations of inverted files, Btrees, prefix Btrees, suffix arrays, compacted tries and suffix trees. String Btrees have the same worstcase performance as Btrees but they manage unboundedlength strings and perform much more powerful search operations such as the ones supported by suffix trees. String Btrees are also effective in main memory (RAM model) because they improve the online suffix tree search on a dynamic set of strings. They also can be successfully applied to database indexing and software duplication.
Orthogonal range reporting in three and higher dimensions
 In Proc. 50th IEEE Symposium on Foundations of Computer Science
, 2009
"... In orthogonal range reporting we are to preprocess N points in ddimensional space so that the points inside a ddimensional axisaligned query box can be reported efficiently. This is a fundamental problem in various fields, including spatial databases and computational geometry. In this paper we p ..."
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Cited by 9 (7 self)
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In orthogonal range reporting we are to preprocess N points in ddimensional space so that the points inside a ddimensional axisaligned query box can be reported efficiently. This is a fundamental problem in various fields, including spatial databases and computational geometry. In this paper we provide a number of improvements for three and higher dimensional orthogonal range reporting: In the pointer machine model, we improve all the best previous results, some of which have not seen any improvements in almost two decades. In the I/Omodel, we improve the previously known threedimensional structures and provide the first (nontrivial) structures for four and higher dimensions. Keywordsdata structures; computational geometry; orthogonal range searching; external memory; 1.
An optimal dynamic interval stabbingmax data structure
 In Proc. ACMSIAM Symposium on Discrete Algorithms
, 2005
"... 1 Introduction In this paper we consider data structures for thestabbingmax problem (also sometimes called the rectangle intersection with priorities problem). That is, theproblem of dynamically maintaining a set S of n axisparallel hyperrectangles in Rd, where each rectangle s 2 S has a weight w ..."
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Cited by 7 (2 self)
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1 Introduction In this paper we consider data structures for thestabbingmax problem (also sometimes called the rectangle intersection with priorities problem). That is, theproblem of dynamically maintaining a set S of n axisparallel hyperrectangles in Rd, where each rectangle s 2 S has a weight w(s) 2 R, so that the rectangle withthe maximum weight containing a query point can be
Higherdimensional orthogonal range reporting and rectangle stabbing in the pointer machine model
 In Proc. 28th ACM Symposium on Computational Geometry
, 2012
"... In this paper, we consider two fundamental problems in the pointer machine model of computation, namely orthogonal range reporting and rectangle stabbing. Orthogonal range reporting is the problem of storing a set of n points in ddimensional space in a data structure, such that the t points in an a ..."
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Cited by 2 (2 self)
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In this paper, we consider two fundamental problems in the pointer machine model of computation, namely orthogonal range reporting and rectangle stabbing. Orthogonal range reporting is the problem of storing a set of n points in ddimensional space in a data structure, such that the t points in an axisaligned query rectangle can be reported efficiently. Rectangle stabbing is the “dual ” problem where a set of n axisaligned rectangles should be stored in a data structure, such that the t rectangles that contain a query point can be reported efficiently. Very recently an optimal O(log n + t) query time pointer machine data structure was developed for the threedimensional version of the orthogonal range reporting problem. However, in four dimensions the best known query bound of O(log 2 n / log log n + t) has not been improved for decades. We describe an orthogonal range reporting data structure that is the first structure to achieve significantly less than O(log 2 n + t) query time in four dimensions. More precisely, we develop a structure that uses O(n(log n / log log n) d) space and can answer ddimensional orthogonal range reporting queries (for d ≥ 4) in O(log n(log n / log log n) d−4+1/(d−2) +t) time. Ignoring log log n factors, this speeds up the best previous query time by a log 1−1/(d−2) n factor. For the rectangle stabbing problem, we show that any data structure that uses nh space must use Ω(log n(log n / log h) d−2 + t) time
Improved Range Searching Lower Bounds
"... In this paper we present a number of improved lower bounds for range searching in the pointer machine and the group model. In the pointer machine, we prove lower bounds for the approximate simplex range reporting problem. In approximate simplex range reporting, points that lie within a distance of ε ..."
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In this paper we present a number of improved lower bounds for range searching in the pointer machine and the group model. In the pointer machine, we prove lower bounds for the approximate simplex range reporting problem. In approximate simplex range reporting, points that lie within a distance of ε · diam(s) from the border of a query simplex s, are free to be included or excluded from the output, where ε ≥ 0 is an input parameter to the range searching problem. We prove our lower bounds by constructing a hard input set and query set, and then invoking Chazelle and Rosenberg’s [CGTA’96] general theorem on the complexity of navigation in the pointer machine. For the group model, we show that input sets and query sets that are hard for range reporting in the pointer machine (i.e. by Chazelle and Rosenberg’s theorem), are also hard for dynamic range searching in the group model. This theorem allows us to reuse decades of research on range reporting lower bounds to immediately obtain a range of new group model lower bounds. Amongst others, this includes an improved lower bound for the fundamental problem of dynamic ddimensional orthogonal range searching, stating that tqtu = Ω((lg n / lg lg n) d−1). Here tq denotes the query time and tu the update time of the data structure. This is an improvement of a lg 1−δ n factor over the recent lower bound of Larsen [FOCS’11], where δ> 0 is a small constant depending on the dimension.
Models and Techniques for Proving Data Structure Lower Bounds
, 2013
"... In this dissertation, we present a number of new techniques and tools for proving lower bounds on the operational time of data structures. These techniques provide new lines of attack for proving lower bounds in both the cell probe model, the group model, the pointer machine model and the I/Omodel. ..."
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In this dissertation, we present a number of new techniques and tools for proving lower bounds on the operational time of data structures. These techniques provide new lines of attack for proving lower bounds in both the cell probe model, the group model, the pointer machine model and the I/Omodel. In all cases, we push the frontiers further by proving lower bounds higher than what could possibly be proved using previously known techniques. For the cell probe model, our results have the following consequences: • The first Ω(lg n) query time lower bound for linear space static data structures. The highest previous lower bound for any static data structure problem peaked at Ω(lg n / lg lg n). • An Ω((lg n / lg lg n) 2) lower bound on the maximum of the update time and the query time of dynamic data structures. This is almost a quadratic improvement over the highest previous lower bound of Ω(lg n). In the group model, we establish a number of intimate connections to the fields of combinatorial discrepancy and range reporting in the pointer machine
I/O Efficient Orthogonal Range Reporting in Three and Higher Dimensions
"... In orthogonal range reporting we are to preprocess N points in d dimensions such that the points inside an axisaligned query box can be found efficiently. This is a fundamental problem in various fields, including spatial databases and computational geometry. In this paper we construct the first da ..."
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In orthogonal range reporting we are to preprocess N points in d dimensions such that the points inside an axisaligned query box can be found efficiently. This is a fundamental problem in various fields, including spatial databases and computational geometry. In this paper we construct the first data structure for orthogonal range reporting in the I/Omodel in higher dimensions and also significantly improve the best previous space lower bound.
ABSTRACT I/OEfficient Batched UnionFind and Its Applications to Terrain Analysis ∗
"... Despite extensive study over the last four decades and numerous applications, no I/Oefficient algorithm is known for the unionfind problem. In this paper we present an I/Oefficient algorithm for the batched (offline) version of the unionfind problem. Given any sequence of N union and find opera ..."
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Despite extensive study over the last four decades and numerous applications, no I/Oefficient algorithm is known for the unionfind problem. In this paper we present an I/Oefficient algorithm for the batched (offline) version of the unionfind problem. Given any sequence of N union and find operations, where each union operation joins two distinct sets, our algorithm uses O(SORT(N)) =