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29
Marked Ancestor Problems
, 1998
"... Consider a rooted tree whose nodes can be marked or unmarked. Given a node, we want to find its nearest marked ancestor. This generalises the wellknown predecessor problem, where the tree is a path. ..."
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Cited by 52 (7 self)
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Consider a rooted tree whose nodes can be marked or unmarked. Given a node, we want to find its nearest marked ancestor. This generalises the wellknown predecessor problem, where the tree is a path.
Rank modulation for flash memories
, 2009
"... We explore a novel data representation scheme for multilevel flash memory cells, in which a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. The only allowed chargeplacement mechanism is a “pushtothetop” operation, which takes a ..."
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Cited by 44 (24 self)
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We explore a novel data representation scheme for multilevel flash memory cells, in which a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. The only allowed chargeplacement mechanism is a “pushtothetop” operation, which takes a single cell of the set and makes it the topcharged cell. The resulting scheme eliminates the need for discrete cell levels, as well as overshoot errors, when programming cells. We present unrestricted Gray codes spanning all possible ncell states and using only “pushtothetop” operations, and also construct balanced Gray codes. One important application of the Gray codes is the realization of logic multilevel cells, which is useful in conventional storage solutions. We also investigate rewriting schemes for random data modification. We present both an optimal scheme for the worst case rewrite performance and an approximation scheme for the averagecase rewrite performance.
Logarithmic lower bounds in the cellprobe model
 SIAM Journal on Computing
"... Abstract. We develop a new technique for proving cellprobe lower bounds on dynamic data structures. This enables us to prove Ω(lg n) bounds, breaking a longstanding barrier of Ω(lg n/lg lg n). We can also prove the first Ω(lgB n) lower bound in the external memory model, without assumptions on the ..."
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Cited by 34 (4 self)
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Abstract. We develop a new technique for proving cellprobe lower bounds on dynamic data structures. This enables us to prove Ω(lg n) bounds, breaking a longstanding barrier of Ω(lg n/lg lg n). We can also prove the first Ω(lgB n) lower bound in the external memory model, without assumptions on the data structure. We use our technique to prove better bounds for the partialsums problem, dynamic connectivity and (by reductions) other dynamic graph problems. Our proofs are surprisingly simple and clean. The bounds we obtain are often optimal, and lead to a nearly complete understanding of the problems. We also present new matching upper bounds for the partialsums problem. Key words. cellprobe complexity, lower bounds, data structures, dynamic graph problems, partialsums problem AMS subject classification. 68Q17
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 29 (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
Ranking and Unranking Permutations in Linear Time
 Information Processing Letters
, 2000
"... A ranking function for the permutations on n symbols assigns a unique integer in the range [0; n!\Gamma1] to each of the n! permutations. The corresponding unranking function is the inverse: given an integer between 0 and n!\Gamma1, the value of the function is the permutation having this rank. W ..."
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Cited by 26 (0 self)
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A ranking function for the permutations on n symbols assigns a unique integer in the range [0; n!\Gamma1] to each of the n! permutations. The corresponding unranking function is the inverse: given an integer between 0 and n!\Gamma1, the value of the function is the permutation having this rank. We present simple ranking and unranking algorithms for permutations that can be computed using O(n) arithmetic operations. Keywords: permutation, ranking, unranking, algorithms for combinatorial problems. 1 Historical Background A permutation of order n is an arrangement of n symbols. For convenience when applying modular arithmetic, this paper considers permutations of f0; 1; 2; :::; n\Gamma1g. The set of all permutations over f0; 1; 2; :::; n\Gamma1g is denoted by S n . There are many applications that call for an array indexed by the permutations in S n [2]. One example is the development of programs that search for Hamilton cycles in particular types of Cayley graphs [10, 11]. To do...
Succinct Dynamic Data Structures
"... We develop succinct data structures to represent (i) a sequence of values to support partial sum and select queries and update (changing values) and (ii) a dynamic array consisting of a sequence of elements which supports insertion, deletion and access of an element at any given index. For the parti ..."
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Cited by 25 (2 self)
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We develop succinct data structures to represent (i) a sequence of values to support partial sum and select queries and update (changing values) and (ii) a dynamic array consisting of a sequence of elements which supports insertion, deletion and access of an element at any given index. For the partial sums problem...
Optimal Biweighted Binary Trees And The Complexity Of Maintaining Partial Sums
 SIAM Journal on Computing
, 1998
"... . Let A be an array. The partial sum problem concerns the design of a data structure for implementing the following operations. The operation update(j, x) has the e#ect ..."
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Cited by 16 (0 self)
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.<F3.849e+05> Let<F3.187e+05> A<F3.849e+05> be an array. The<F3.262e+05> partial sum problem<F3.849e+05> concerns the design of a data structure for implementing the following operations. The operation<F3.187e+05> update(j,<F3.849e+05> x) has the e#ect<F3.187e+05><F3.849e+05><F3.187e+05><F3.849e+05> A[j]<F5.57e+05> #<F3.187e+05><F3.849e+05><F3.187e+05><F3.849e+05><F3.187e+05> A[j]+x<F3.849e+05> , and the query operation<F3.187e+05><F3.849e+05> sum(j) returns the partial sum<F7.1e+05> #<F1.882e+05> j<F2.831e+05> i=1<F3.187e+05><F3.849e+05><F3.187e+05><F3.849e+05> A[i] . Our interest centers upon the optimal e#ciency with which sequences of such operations can be performed, and we derive new upper and lower bounds in the semigroup model of computation. Our analysis relates the optimal complexity of the partial sum problem to optimal binary trees relative to a type of weighting scheme that defines the notion of<F3.262e+05> biweighted<F3.849e+05> binary tree.<F4.005e+05> Key words.<F3...
Lower bounds for dynamic connectivity
 STOC
, 2004
"... We prove an Ω(lg n) cellprobe lower bound on maintaining connectivity in dynamic graphs, as well as a more general tradeoff between updates and queries. Our bound holds even if the graph is formed by disjoint paths, and thus also applies to trees and plane graphs. The bound is known to be tight fo ..."
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Cited by 15 (0 self)
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We prove an Ω(lg n) cellprobe lower bound on maintaining connectivity in dynamic graphs, as well as a more general tradeoff between updates and queries. Our bound holds even if the graph is formed by disjoint paths, and thus also applies to trees and plane graphs. The bound is known to be tight for these restricted cases, proving optimality of these data structures (e.g., Sleator and Tarjan’s dynamic trees). Our tradeoff is known to be tight for trees, and the best two data structures for dynamic connectivity in general graphs are points on our tradeoff curve. In this sense these two data structures are optimal, and this tightness serves as strong evidence that our lower bounds are the best possible. From a more theoretical perspective, our result is the first logarithmic cellprobe lower bound for any problem in the natural class of dynamic language membership problems, breaking the long standing record of Ω(lg n / lg lg n). In this sense, our result is the first datastructure lower bound that is “truly ” logarithmic, i.e., logarithmic in the problem size counted in bits. Obtaining such a bound is listed as one of three major challenges for future research by Miltersen [13] (the other two challenges remain unsolved). Our techniques form a general framework for proving cellprobe lower bounds on dynamic data structures. We show how our framework also applies to the partialsums problem to obtain a nearly complete understanding of the problem in cellprobe and algebraic models, solving several previously posed open problems.