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Membership in constant time and almostminimum space
 SIAM Journal on Computing
, 1999
"... Abstract. This paper deals with the problem of storing a subset of elements from the bounded universeM = {0,...,M−1} so that membership queries can be performed efficiently. In particular, we introduce a data structure to represent a subset of N elements of M in a number of bits close to the informa ..."
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Cited by 69 (1 self)
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Abstract. This paper deals with the problem of storing a subset of elements from the bounded universeM = {0,...,M−1} so that membership queries can be performed efficiently. In particular, we introduce a data structure to represent a subset of N elements of M in a number of bits close to the informationtheoretic minimum, B = lg
Are bitvectors optimal?
"... ... We show lower bounds that come close to our upper bounds (for a large range of n and ffl): Schemes that answer queries with just one bitprobe and error probability ffl must use \Omega ( nffl log(1=ffl) log m) bits of storage; if the error is restricted to queries not in S, then the scheme must u ..."
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Cited by 49 (7 self)
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... We show lower bounds that come close to our upper bounds (for a large range of n and ffl): Schemes that answer queries with just one bitprobe and error probability ffl must use \Omega ( nffl log(1=ffl) log m) bits of storage; if the error is restricted to queries not in S, then the scheme must use \Omega ( n2ffl2 log(n=ffl) log m) bits of storage. We also
Lower bounds for UnionSplitFind related problems on random access machines
, 1994
"... We prove \Omega\Gamma p log log n) lower bounds on the random access machine complexity of several dynamic, partially dynamic and static data structure problems, including the unionsplitfind problem, dynamic prefix problems and onedimensional range query problems. The proof techniques include a ..."
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Cited by 48 (3 self)
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We prove \Omega\Gamma p log log n) lower bounds on the random access machine complexity of several dynamic, partially dynamic and static data structure problems, including the unionsplitfind problem, dynamic prefix problems and onedimensional range query problems. The proof techniques include a general technique using perfect hashing for reducing static data structure problems (with a restriction of the size of the structure) into partially dynamic data structure problems (with no such restriction), thus providing a way to transfer lower bounds. We use a generalization of a method due to Ajtai for proving the lower bounds on the static problems, but describe the proof in terms of communication complexity, revealing a striking similarity to the proof used by Karchmer and Wigderson for proving lower bounds on the monotone circuit depth of connectivity. 1 Introduction and summary of results In this paper we give lower bounds for the complexity of implementing several dynamic and sta...
The Cell Probe Complexity of Succinct Data Structures
 In Automata, Languages and Programming, 30th International Colloquium (ICALP 2003
, 2003
"... We show lower bounds in the cell probe model for the redundancy/query time tradeoff of solutions to static data structure problems. ..."
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Cited by 30 (0 self)
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We show lower bounds in the cell probe model for the redundancy/query time tradeoff of solutions to static data structure problems.
Cell probe complexity  a survey
 In 19th Conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 1999. Advances in Data Structures Workshop
"... The cell probe model is a general, combinatorial model of data structures. We give a survey of known results about the cell probe complexity of static and dynamic data structure problems, with an emphasis on techniques for proving lower bounds. 1 ..."
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Cited by 28 (0 self)
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The cell probe model is a general, combinatorial model of data structures. We give a survey of known results about the cell probe complexity of static and dynamic data structure problems, with an emphasis on techniques for proving lower bounds. 1
Membership in Constant Time and Minimum Space
 Lecture Notes in Computer Science
, 1994
"... . We investigate the problem of storing a subset of the elements of a boundeduniverse so that searches canbe performed in constant time and the space used is within a constant factor of the minimum required. Initially we focus on the static version of this problem and conclude with an enhancement th ..."
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Cited by 20 (6 self)
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. We investigate the problem of storing a subset of the elements of a boundeduniverse so that searches canbe performed in constant time and the space used is within a constant factor of the minimum required. Initially we focus on the static version of this problem and conclude with an enhancement that permits insertions and deletions. 1 Introduction Given a universal set M = f0; : : : ; M \Gamma 1g and any subset N = fe 1 ; : : : ; e N g the membership problem is to determine whether given query element in M is an element of N . There are two standard approaches to solve this problem: to list all elements of N (e.g. in a hash table) or to list all the answers (e.g. a bit map of size M ). When N is small the former approach comes close to the information theoretic lower bound on the number of bits needed to represent an arbitrary subset of the given size (i.e. a function of both N and M , l lg \Gamma M N \Delta m ). Similarly, when N is large (say ffM ) the later approach is near...
The Bit Probe Complexity Measure Revisited
 In Proc. 10th Symp. on Theoretical Aspects of Computer Science (STACS
, 1993
"... . A static data structure problem consists of a set of data D, a set of queries Q and a function f with domain D \ThetaQ. Given a space bound b, a (good) solution to the problem is an encoding e : D ! f0; 1g b , so that for any y, f(x; y) can be determined (quickly) by probing e(x). The worst ..."
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Cited by 18 (3 self)
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. A static data structure problem consists of a set of data D, a set of queries Q and a function f with domain D \ThetaQ. Given a space bound b, a (good) solution to the problem is an encoding e : D ! f0; 1g b , so that for any y, f(x; y) can be determined (quickly) by probing e(x). The worst case number of probes needed is C b (f ), the bit probe complexity of f . We study the properties of the complexity measure C b (\Delta). 1 Introduction and preliminaries Elias and Flower [5] introduced the following model of retrieval problems: A set D, called the set of data, a set Q, called the set of queries and a set A, called the set of answers is given, along with a function f : D \Theta Q ! A. The problem is to devise a scheme for encoding elements of D into data structures in the memory of a random access machine. When an x 2 D has been encoded, it should be possible at a later point in time to come forward with any y 2 Q and efficiently compute f(x; y) using random access to...
SpaceTime Tradeoffs for Graph Properties
 In Proceedings of 26th ICALP
, 1999
"... We initiate a study of spacetime tradeoffs in the cellprobe model under restricted preprocessing power. In this setup, we are given: (a) a function f(y; q) where y is the static input and q is a dynamic query, (b) a function family F for preprocessing, and (c) a parameter s indicating the amount o ..."
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Cited by 9 (0 self)
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We initiate a study of spacetime tradeoffs in the cellprobe model under restricted preprocessing power. In this setup, we are given: (a) a function f(y; q) where y is the static input and q is a dynamic query, (b) a function family F for preprocessing, and (c) a parameter s indicating the amount of preprocessing space. The goal is to preprocess the static input y to create a data structure D so that the dynamic queries q can be quickly answered. The data structure D contains s bits of information about y and each bit corresponds to a function in F applied to y. The "time" t to answer a query is measured in terms of the number of bits read from D. Intuitively, this models the situation where the data access is slow/expensive and the local computation is fast/cheap. We study the dependence between the space s and the time t for a given f when preprocessing is done using only functions in F. Classically, spacetime tradeoffs have been studied in this model under the assumption that fam...
This document in subdirectoryRS/03/44/ The Cell Probe Complexity of Succinct Data Structures ∗
, 2003
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS
AN ANALYSIS OF OPTIMAL RETRIEVAL SYSTEMS WITH UPDATES
, 1974
"... The performance of computerimplemented systems for data storage, retrieval, and update is investigated. A data structure is modeled by a set D = {d 1, d. d D of data bases. A set of questions A = {Xlk 2."' about any d E D may be answered. A memory that is bitaddressable by an algorit ..."
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The performance of computerimplemented systems for data storage, retrieval, and update is investigated. A data structure is modeled by a set D = {d 1, d. d D of data bases. A set of questions A = {Xlk 2.&quot;' about any d E D may be answered. A memory that is bitaddressable by an algorithm or an automaton models a computer. A retrieval system is composed of a particular mapping of data bases onto memory representations and a particular algorithm or automaton. By accessing bits of memory the algorithm can answer any X E A about the d represented in memory and can update memory to represent a new d * E D. Lower bounds are derived for the performance measures of storage efficiency, retrieval efficiency, and update efficiency. The minima are simultaneously