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20
Efficient Data Structures for Range Searching on a Grid
, 1987
"... We consider the 2dimensional range searching problem in the case where all point lie on an integer grid. A new data structure is preented that solves range queries on a U U grid in O(k + loglog U) time using O(n log n) storage, where n is the number of points and k the number of reported answers ..."
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Cited by 36 (0 self)
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We consider the 2dimensional range searching problem in the case where all point lie on an integer grid. A new data structure is preented that solves range queries on a U U grid in O(k + loglog U) time using O(n log n) storage, where n is the number of points and k the number of reported answers. Although the query
Improved Behaviour of Tries by Adaptive Branching
"... We introduce and analyze a method to reduce the search cost in tries. Traditional trie structures use branching factors at the nodes that are either fixed or a function of the number of elements. Instead, we let the distribution of the elements guide the choice of branching factors. This is accomp ..."
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Cited by 32 (8 self)
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We introduce and analyze a method to reduce the search cost in tries. Traditional trie structures use branching factors at the nodes that are either fixed or a function of the number of elements. Instead, we let the distribution of the elements guide the choice of branching factors. This is accomplished in a strikingly simple way: in a binary trie, the i highest complete levels are replaced by a single node of degree 2i; the compression is repeated in the subtries. This structure, the levelcompressed trie, inherits the good properties of binary tries with respect to neighbour and range searches, while the external path length is significantly decreased. It also has the advantage of being easy to implement. Our analysis shows that the expected depth of a stored element is \Theta (log \Lambda n) for uniformly distributed data.
Repetitionbased text indexes
, 1999
"... fast pattern matching queries. The scheme provides a general framework for representing information about repetitions, i.e., multiple occurrences of the same string in the text, and for using the information in pattern matching. Wellknown text indexes, such as suffix trees, suffix arrays, DAWGs and ..."
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Cited by 27 (0 self)
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fast pattern matching queries. The scheme provides a general framework for representing information about repetitions, i.e., multiple occurrences of the same string in the text, and for using the information in pattern matching. Wellknown text indexes, such as suffix trees, suffix arrays, DAWGs and their variations, which we collectively call suffix indexes, can be seen as instances of the scheme.
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.
Confluently Persistent Deques via DataStructural Bootstrapping
 J. of Algorithms
, 1993
"... We introduce datastructural bootstrapping, a technique to design data structures recursively, and use it to design confluently persistent deques. Our data structure requires O(log 3 k) worstcase time and space per deletion, where k is the total number of deque operations, and constant worstcase t ..."
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Cited by 15 (4 self)
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We introduce datastructural bootstrapping, a technique to design data structures recursively, and use it to design confluently persistent deques. Our data structure requires O(log 3 k) worstcase time and space per deletion, where k is the total number of deque operations, and constant worstcase time and space for other operations. Further, the data structure allows a purely functional implementation, with no side effects. This improves a previous result of Driscoll, Sleator, and Tarjan. 1 An extended abstract of this paper was presented at the 4th ACMSIAM Symposium on Discrete Algorithms, 1993. 2 Supported by a Fannie and John Hertz Foundation fellowship, National Science Foundation Grant No. CCR8920505, and the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) under NSFSTC8809648. 3 Also affiliated with NEC Research Institute, 4 Independence Way, Princeton, NJ 08540. Research at Princeton University partially supported by the National Science Foundatio...
Bounded Ordered Dictionaries in O(log log N) Time and O(n) Space
 Information Processing Letters
, 1990
"... In this paper we show how to implement bounded ordered dictionaries, also called bounded priority queues, in O(log log N) time per operation and O(n) space. Here n denotes the number of elements stored in the dictionary and N denotes the size of the universe. Previously, this time bound required O(N ..."
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Cited by 14 (0 self)
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In this paper we show how to implement bounded ordered dictionaries, also called bounded priority queues, in O(log log N) time per operation and O(n) space. Here n denotes the number of elements stored in the dictionary and N denotes the size of the universe. Previously, this time bound required O(N) space [E77].
Efficient dynamic methodlookup for object oriented languages (Extended Abstract)
, 1996
"... ) Paolo Ferragina 1 and S. Muthukrishnan 2 1 Dipartimento di Informatica, Universit`a di Pisa, Italy. ferragin@di.unipi.it 2 Dept. of Computer Science, Univ. of Warwick, UK. muthu@dcs.warwick.ac.uk 1 Introduction We consider the following dynamic data structural problem. We are given a rooted ..."
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Cited by 11 (1 self)
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) Paolo Ferragina 1 and S. Muthukrishnan 2 1 Dipartimento di Informatica, Universit`a di Pisa, Italy. ferragin@di.unipi.it 2 Dept. of Computer Science, Univ. of Warwick, UK. muthu@dcs.warwick.ac.uk 1 Introduction We consider the following dynamic data structural problem. We are given a rooted tree of n nodes and a set f1; 2; : : :; Cg of colors. Each node u has a subset of these colors, say of size d u , and P u du = D. Note D C. The problem is to dynamically maintain this tree under updates, that is, insert(p; c) and delete(p; c) operations, and answer find(p; c) queries. The operations insert(p; c) and delete(p; c) respectively add and remove the color c from the node pointed to by pointer p (the tree does not change topology under these dynamic operations). The find(p; c) query returns the nearest ancestor, if any, of the node pointed to by p (possibly that node itself) which has the color c, 1 c C. If no such ancestor exists, Find(p; c) returns Null. We call this the...
Compressed dictionaries: Space measures, data sets, and experiments
 In Proc. 5th International Workshop on Experimental Algorithms (WEA
, 2006
"... Abstract. In this paper, we present an experimental study of the spacetime tradeoffs for the dictionary problem, where we design a data structure to represent set data, which consist of a subset S of n items out of a universe U = {0, 1,...,u − 1} supporting various queries on S. Our primary goal is ..."
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Cited by 8 (1 self)
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Abstract. In this paper, we present an experimental study of the spacetime tradeoffs for the dictionary problem, where we design a data structure to represent set data, which consist of a subset S of n items out of a universe U = {0, 1,...,u − 1} supporting various queries on S. Our primary goal is to reduce the space required for such a dictionary data structure. Many compression schemes have been developed for dictionaries, which fall generally in the categories of combinatorial encodings and dataaware methods and still support queries efficiently. We show that for many (realworld) datasets, dataaware methods lead to a worthwhile compression over combinatorial methods. Additionally, we design a new dataaware building block structure called BSGAP that presents improvements over other dataaware methods. 1
An Old SubQuadratic Algorithm for Finding Extremal Sets
, 1994
"... Some previously proposed algorithms are reexamined. They were designed to find all sets in a collection that have no subset in the collection, but are easily modified to find all sets that have no supersets. One is shown to have a worstcase runningtime of O(N 2 = log N ), where N is the sum of ..."
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Cited by 6 (3 self)
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Some previously proposed algorithms are reexamined. They were designed to find all sets in a collection that have no subset in the collection, but are easily modified to find all sets that have no supersets. One is shown to have a worstcase runningtime of O(N 2 = log N ), where N is the sum of the sizes of all the sets. This is lower than the only previously known subquadratic worstcase upper bound for this problem. Key words: Analysis of algorithms, settheoretic algorithms, extremal sets. 1 Introduction Yellin and Jutla [3] tackled the following fundamental problem, for some applications of which see [2]. Given is a collection F = fS 1 ; : : : ; S k g, where each S i is a set over the same domain. A set is a minimal (resp. maximal) set of F iff it has no strict subset (resp. superset) in F . Find the extremal sets of F , i.e., those that are minimal or maximal. With the problem size chosen as N = P i S i , Yellin and Jutla presented an abstract algorithm that requires O(N ...
Threedimensional layers of maxima
 Algorithmica
"... Abstract. We present an O(n log n)time algorithm to solve the threedimensional layersofmaxima problem, an improvement over the prior O(n log n log log n)time solution. A previous claimed O(n log n)time solution due to Atallah, Goodrich, and Ramaiyer [SCG’94] has technical flaws. Our algorithm i ..."
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Abstract. We present an O(n log n)time algorithm to solve the threedimensional layersofmaxima problem, an improvement over the prior O(n log n log log n)time solution. A previous claimed O(n log n)time solution due to Atallah, Goodrich, and Ramaiyer [SCG’94] has technical flaws. Our algorithm is based on a common framework underlying previous work, but to implement it we devise a new data structure to solve a special case of dynamic planar point location in a staircase subdivision. Our data structure itself relies on a new extension to dynamic fractional cascading that allows vertices of high degree in the control graph. 1