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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
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 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
The quantum complexity of set membership
 In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science
, 2000
"... We study the quantum complexity of the static set membership problem: given a subset S (S  ≤ n) of a universe of size m ( ≫ n), store it as a table, T: {0,1} r → {0,1}, of bits so that queries of the form ‘Is x in S? ’ can be answered. The goal is to use a small table and yet answer queries using ..."
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Cited by 8 (2 self)
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We study the quantum complexity of the static set membership problem: given a subset S (S  ≤ n) of a universe of size m ( ≫ n), store it as a table, T: {0,1} r → {0,1}, of bits so that queries of the form ‘Is x in S? ’ can be answered. The goal is to use a small table and yet answer queries using few bit probes. This problem was considered recently by Buhrman, Miltersen, Radhakrishnan and Venkatesh [BMRV00], who showed lower and upper bounds for this problem in the classical deterministic and randomised models. In this paper, we formulate this problem in the “quantum bit probe model”. We assume that access to the table T is provided by means of a black box (oracle) unitary transform OT that takes the basis state y,b 〉 to the basis state y,b⊕T(y)〉. The query algorithm is allowed to apply OT on any superposition of basis states. We show tradeoff results between space (defined as 2 r) and number of probes (oracle calls) in this model. Our results show that the lower bounds shown in [BMRV00] for the classical model also hold (with minor differences) in the quantum bit probe model. These bounds almost match the classical upper bounds. Our lower bounds are proved using linear algebraic arguments.