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18
New data structures for orthogonal range searching
 In Proc. 41st IEEE Symposium on Foundations of Computer Science
, 2000
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Tight(er) worstcase bounds on dynamic searching and priority queues
 In Proc. 32nd ACM Symposium on Theory of Computing (STOC
, 2000
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On Sorting Strings in External Memory
, 1997
"... ) Lars Arge Paolo Ferragina y Roberto Grossi z Jeffrey Scott Vitter x Abstract. In this paper we address for the first time the I/O complexity of the problem of sorting strings in external memory, which is a fundamental component of many largescale text applications. In the standard unitcost RAM c ..."
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Cited by 27 (12 self)
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) Lars Arge Paolo Ferragina y Roberto Grossi z Jeffrey Scott Vitter x Abstract. In this paper we address for the first time the I/O complexity of the problem of sorting strings in external memory, which is a fundamental component of many largescale text applications. In the standard unitcost RAM comparison model, the complexity of sorting K strings of total length N is \Theta(K log 2 K+N). By analogy, in the external memory (or I/O) model, where the internal memory has size M and the block transfer size is B, it would be natural to guess that the I/O complexity of sorting strings is \Theta( K B log M=B K B + N B ), but the known algorithms do not come even close to achieving this bound. Our results show, somewhat counterintuitively, that the I/O complexity of string sorting depends upon the length of the strings relative to the block size. We first consider a simple comparison I/O model, where one is not allowed to break the strings into their characters, and we sho...
Improved shortest paths on the word RAM
 IN: 27TH COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP), IN: LECTURE NOTES IN COMPUT. SCI
, 2000
"... Thorup recently showed that singlesource shortestpaths problems in undirected networks with n vertices, m edges, and edge weights drawn from {0,...,2 w − 1} can be solved in O(n + m) time and space on a unitcost randomaccess machine with a word length of w bits. His algorithm works by traversin ..."
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Cited by 24 (0 self)
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Thorup recently showed that singlesource shortestpaths problems in undirected networks with n vertices, m edges, and edge weights drawn from {0,...,2 w − 1} can be solved in O(n + m) time and space on a unitcost randomaccess machine with a word length of w bits. His algorithm works by traversing a socalled component tree. Two new related results are provided here. First, and most importantly, Thorup’s approach is generalized from undirected to directed networks. The resulting time bound, O(n + m log w), is the best deterministic linearspace bound known for sparse networks unless w is superpolynomial in log n. As an application, allpairs shortestpaths problems in directed networks with n vertices, m edges, and edge weights in {−2 w,...,2 w} can be solved in O(nm + n 2 log log n) time and O(n + m) space (not counting the output space). Second, it is shown that the component tree for an undirected network can be constructed in deterministic linear time and space with a simple algorithm, to be contrasted with a complicated and impractical solution suggested by Thorup. Another contribution of the present paper is a greatly simplified view of the principles underlying algorithms based on component trees.
Static Dictionaries on AC^0 RAMs: Query time Θ(,/log n / log log n) is necessary and sufficient
, 1996
"... In this paper we consider solutions to the static dictionary problem ���� � on RAMs, i.e. random access machines where the only restriction on the finite instruction set is that all computational instructions are ���� � in. Our main result is a tight upper and lower bound ���� � ���©���������������� ..."
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Cited by 19 (5 self)
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In this paper we consider solutions to the static dictionary problem ���� � on RAMs, i.e. random access machines where the only restriction on the finite instruction set is that all computational instructions are ���� � in. Our main result is a tight upper and lower bound ���� � ���©��������������������� of on the time for answering membership queries in a set of � size when reasonable space is used for the data structure storing the set; the upper bound can be obtained using space ������ � �� � ���� �. Several variations of this result are also obtained. Among others, we show a tradeoff between time and circuit depth under the unitcost assumption: any RAM instruction set which permits a linear space, constant query time solution to the static dictionary problem must have an instruction of depth �������©���������������©���� � , where � is the word size of the machine (and ���© � the size of the universe). This matches the depth of multiplication and integer division, used in the perfect hashing scheme by Fredman, Komlós and Szemerédi.
Subquadratic algorithms for 3SUM
 In Proc. 9th Worksh. Algorithms & Data Structures, LNCS 3608
, 2005
"... We obtain subquadratic algorithms for 3SUM on integers and rationals in several models. On a standard word RAM with wbit words, we obtain a running time of O(n 2 / max { w lg 2 w, lg 2 n (lg lg n) 2}). In the circuit RAM with one nonstandard AC0 operation, we obtain O(n2 / w2 lg2). In external w me ..."
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Cited by 12 (2 self)
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We obtain subquadratic algorithms for 3SUM on integers and rationals in several models. On a standard word RAM with wbit words, we obtain a running time of O(n 2 / max { w lg 2 w, lg 2 n (lg lg n) 2}). In the circuit RAM with one nonstandard AC0 operation, we obtain O(n2 / w2 lg2). In external w memory, we achieve O(n2 /(MB)), even under the standard assumption of data indivisibility. Cacheobliviously, we obtain a running time of O(n2 / MB lg2). In all cases, our speedup is almost M quadratic in the parallelism the model can afford, which may be the best possible. Our algorithms are Las Vegas randomized; time bounds hold in expectation, and in most cases, with high probability. 1
On sorting strings in external memory (Extended Abstract)
 IN STOC ’97: PROCEEDINGS OF THE TWENTYNINTH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1997
"... In this paper we address for the first time the I/O complexity of the problem of sorting strings in external memory, which is a fundamental component of many largescale text applications. In the standard unitcost RAM comparison model, the complexity of sorting K strings of total length N is (K log ..."
Abstract

Cited by 4 (0 self)
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In this paper we address for the first time the I/O complexity of the problem of sorting strings in external memory, which is a fundamental component of many largescale text applications. In the standard unitcost RAM comparison model, the complexity of sorting K strings of total length N is (K log2 K +N). By analogy, in the external memory (or I/O) model, where the internal memory has size M and the block transfer size is B, it would be natural to guess that the I/O complexity of sorting strings is ( K B logM=B K N
Four soviets walk the dog  with an application to Alt’s conjecture
 CORR
"... Given two polygonal curves in the plane, there are many ways to define a notion of similarity between them. One measure that is extremely popular is the Fréchet distance. Since it has been proposed by Alt and Godau in 1992, many variants and extensions have been studied. Nonetheless, even more than ..."
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Cited by 3 (1 self)
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Given two polygonal curves in the plane, there are many ways to define a notion of similarity between them. One measure that is extremely popular is the Fréchet distance. Since it has been proposed by Alt and Godau in 1992, many variants and extensions have been studied. Nonetheless, even more than 20 years later, the original O(n 2 log n) algorithm by Alt and Godau for computing the Fréchet distance remains the state of the art (here n denotes the number of vertices on each curve). This has led Helmut Alt to conjecture that the associated decision problem is 3SUMhard. In recent work, Agarwal et al. show how to break the quadratic barrier for the discrete version of the Fréchet distance, where one considers sequences of points instead of polygonal curves. Building on their work, we give a randomized algorithm to compute the Fréchet distance between two polygonal curves in time O(n 2 √ log n(log log n) 3/2) on a pointer machine and in time O(n 2 (log log n) 2) on a word RAM. Furthermore, we show that there exists an algebraic decision tree for the decision problem of depth O(n 2−ε), for some ε> 0. This provides evidence that the decision problem may not be 3SUMhard after all and reveals an intriguing new aspect of this wellstudied problem.
An Enhancement of Major Sorting Algorithms
, 2008
"... Abstract: One of the fundamental issues in computer science is ordering a list of items. Although there is a huge number of sorting algorithms, sorting problem has attracted a great deal of research; because efficient sorting is important to optimize the use of other algorithms. This paper presents ..."
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Cited by 2 (0 self)
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Abstract: One of the fundamental issues in computer science is ordering a list of items. Although there is a huge number of sorting algorithms, sorting problem has attracted a great deal of research; because efficient sorting is important to optimize the use of other algorithms. This paper presents two new sorting algorithms, enhanced selection sort and enhanced bubble Sort algorithms. Enhanced selection sort is an enhancement on selection sort by making it slightly faster and stable sorting algorithm. Enhanced bubble sort is an enhancement on both bubble sort and selection sort algorithms with O(nlgn) complexity instead of O(n 2) for bubble sort and selection sort algorithms. The two new algorithms are analyzed, implemented, tested, and compared and the results were promising.
Klee’s measure problem made easy
, 2013
"... We present a new algorithm for a classic problem in computational geometry, Klee’s measure problem: given a set of n axisparallel boxes in ddimensional space, compute the volume of the union of the boxes. The algorithm runs in O(n d/2) time for any constant d ≥ 3. Although it improves the previous ..."
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Cited by 1 (1 self)
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We present a new algorithm for a classic problem in computational geometry, Klee’s measure problem: given a set of n axisparallel boxes in ddimensional space, compute the volume of the union of the boxes. The algorithm runs in O(n d/2) time for any constant d ≥ 3. Although it improves the previous best algorithm by “just ” an iterated logarithmic factor, the real surprise lies in the simplicity of the new algorithm. We also show that it is theoretically possible to beat the O(n d/2) time bound by logarithmic factors for integer input in the word RAM model, and for other variants of the problem. With additional work, we obtain an O(n d/3 polylog n)time algorithm for the important special case of orthants or unit hypercubes (which include the socalled “hypervolume indicator problem”), and an O(n (d+1)/3 polylog n)time algorithm for the case of arbitrary hypercubes or fat boxes, improving a previous O(n (d+2)/3)time algorithm by Bringmann. 1