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17
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 57 (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
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.
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 49 (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...
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
Searching Constant Width Mazes Captures the AC° Hierarchy
 In Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
, 1997
"... We show that searching a width /' maze is complete for II, i.e., for the /"th level of the AC hierarchy. Equivalently, stconnectivity for width /' grid graphs is complete for II. As an application, we show that there is a data structure solving dynamic stconnectivity for constant width grid gr ..."
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Cited by 22 (4 self)
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We show that searching a width /' maze is complete for II, i.e., for the /"th level of the AC hierarchy. Equivalently, stconnectivity for width /' grid graphs is complete for II. As an application, we show that there is a data structure solving dynamic stconnectivity for constant width grid graphs with time bound O (log log n) per operation on a random access machine. The dynamic algorithm is derived from the parallel one in an indirect way using algebraic tools.
Dynamic Algorithms for the Dyck Languages
 IN PROC. 4TH WORKSHOP ON ALGORITHMS AND DATA STRUCTURES (WADS
, 1995
"... We study dynamic membership problems for the Dyck languages, the class of strings of properly balanced parentheses. We also study the Dynamic Word problem for the free group. We present deterministic algorithms and data structures which maintain a string under replacements of symbols, insertions ..."
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Cited by 12 (9 self)
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We study dynamic membership problems for the Dyck languages, the class of strings of properly balanced parentheses. We also study the Dynamic Word problem for the free group. We present deterministic algorithms and data structures which maintain a string under replacements of symbols, insertions, and deletions of symbols, and language membership queries. Updates and queries are handled in polylogarithmic time. We also give both Las Vegas and Monte Carlotype randomised algorithms to achieve better running times, and present lower bounds on the complexity for variants of the problems.
Lower Bounds for Dynamic Transitive Closure, Planar Point Location, and Parentheses Matching
 Nordic Journal of Computing
, 1996
"... We give a number of new lower bounds in the cell probe model with logarithmic cell size, which entails the same bounds on the random access computer with logarithmic word size and unit cost operations. ..."
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Cited by 11 (4 self)
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We give a number of new lower bounds in the cell probe model with logarithmic cell size, which entails the same bounds on the random access computer with logarithmic word size and unit cost operations.
On Searching Sorted Lists: A NearOptimal Lower Bound
, 1997
"... We obtain improved lower bounds for a class of static and dynamic data structure problems that includes several problems of searching sorted lists as special cases. These lower bounds nearly match the upper bounds given by recent striking improvements in searching algorithms given by Fredman and Wil ..."
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Cited by 5 (0 self)
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We obtain improved lower bounds for a class of static and dynamic data structure problems that includes several problems of searching sorted lists as special cases. These lower bounds nearly match the upper bounds given by recent striking improvements in searching algorithms given by Fredman and Willard's fusion trees [9] and Andersson's search data structure [5]. Thus they show sharp limitations on the running time improvements obtainable using the unitcost wordlevel RAM operations that those algorithms employ. 1 Introduction Traditional analysis of problems such as sorting and searching is often schizophrenic in dealing with the operations one is permitted to perform on the input data. In one view, the elements being sorted are seen as abstract objects which may only be compared. In the other view, one is able to perform certain wordlevel operations, such as indirect addressing using the elements themselves, in algorithms like bucket and radix sorting. Traditionally, the second v...
On dynamic bitprobe complexity
, 2005
"... This work present several advances in the understanding of dynamic data structures in the bitprobe model: • We improve the lower bound record for dynamic language membership problems to Ω(( Surpassing Ω(lg n) was listed as the first open problem in a survey by Miltersen. • We prove a bound of Ω( kn ..."
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Cited by 2 (0 self)
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This work present several advances in the understanding of dynamic data structures in the bitprobe model: • We improve the lower bound record for dynamic language membership problems to Ω(( Surpassing Ω(lg n) was listed as the first open problem in a survey by Miltersen. • We prove a bound of Ω( known bounds were Ω( lg n lg lg lg n lg n lg lg n lg n lg lg n)2).) for maintaining partial sums in Z/2Z. Previously, the) and O(lg n). • We prove a surprising and tight upper bound of O ( lg lg n) for the greaterthan problem, and several predecessortype problems. We use this to obtain the same upper bound for dynamic word and prefix problems in groupfree monoids. We also obtain new lower bounds for the partialsums problem in the cellprobe and externalmemory models. Our lower bounds are based on a surprising improvement of the classic chronogram technique of Fredman and Saks [1989], which makes it possible to prove logarithmic lower bounds by this approach. Before the work of M. Pǎtrascu and Demaine [2004], this was the lg n only known technique for dynamic lower bounds, and surpassing Ω ( lg lg n) was a central open problem in cellprobe complexity.
Dynamic Computation
 IAM dournal on Computing
, 1997
"... This thesis is in Theory of Computation. We study quantitative aspects of computational problems that arise in settings where the input instance is subject to changes, i.e., dynamic problems. The results include efficient dynamic algorithms and data structures and strong informationtheoretic lower ..."
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Cited by 1 (0 self)
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This thesis is in Theory of Computation. We study quantitative aspects of computational problems that arise in settings where the input instance is subject to changes, i.e., dynamic problems. The results include efficient dynamic algorithms and data structures and strong informationtheoretic lower bounds for problems on graphs, strings, and finite functions.