Results 1  10
of
15
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 ..."
Abstract

Cited by 49 (7 self)
 Add to MetaCart
... 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
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 ..."
Abstract

Cited by 28 (0 self)
 Add to MetaCart
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
Indexing and Dictionary Matching with One Error (Extended Abstract)
, 1999
"... The indexing problem is the one where a text is preprocessed and subsequent queries of the form: "Find all occurrences of pattern P in the text" are answered in time proportional to the length of the query and the number of occurrences. In the dictionary matching problem a set of patterns ..."
Abstract

Cited by 24 (2 self)
 Add to MetaCart
The indexing problem is the one where a text is preprocessed and subsequent queries of the form: "Find all occurrences of pattern P in the text" are answered in time proportional to the length of the query and the number of occurrences. In the dictionary matching problem a set of patterns is preprocessed and subsequent queries of the form: "Find all occurrences of dictionary patterns in text T" are answered in time proportional to the length of the text and the number of occurrences. There exist efficient worstcase solutions for the indexing problem and the dictionary matching problem, but none that find approximate occurrences of the patterns, i.e. where the pattern is within a bound edit (or hamming...
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 ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
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.
Improved Bounds for Dictionary Lookup with One Error
 Information Processing Letters
, 2000
"... Given a dictionary S of n binary strings each of length m, we consider the problem of designing a data structure for S that supports dqueries; given a binary query string q of length m, a dquery reports if there exists a string in S within Hamming distance d of q. We construct a data structure for ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
Given a dictionary S of n binary strings each of length m, we consider the problem of designing a data structure for S that supports dqueries; given a binary query string q of length m, a dquery reports if there exists a string in S within Hamming distance d of q. We construct a data structure for the case d = 1, that requires space O(n log m) and has query time O(1) in a cell probe model with word size m. This generalizes and improves the previous bounds of Yao and Yao for the problem in the bit probe model. The data structure can be constructed in randomized expected time O(nm). Key words: Data Structures, Dictionaries, Hashing, Hamming Distance 1 Introduction Minsky and Papert in 1969 posed the following problem, that has remained a challenge in data structure design [9]. Let S be a set of n binary strings of length m each. We want to construct a data structure for S that supports fast dqueries; that is, given a binary 1 BRICS (Basic Research in Computer Science), a Center o...
Dictionary LookUp Within Small Edit Distance
 In Proc. 8th Annual Intl. Computing and Combinatorics Conference (COCOON’02
, 2002
"... Let W be a dictionary consisting of n binary strings of length m each, represented as a trie. The usual dquery asks if there exists a string in W within Hamming distance d of a given binary query string q. We present an algorithm to determine if there is a member in W within edit distance d of ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Let W be a dictionary consisting of n binary strings of length m each, represented as a trie. The usual dquery asks if there exists a string in W within Hamming distance d of a given binary query string q. We present an algorithm to determine if there is a member in W within edit distance d of a given query string q of length m. The method takes time O(dm ) in the RAM model, independent of n, and requires O(dm) additional space.
Efficient approximate dictionary lookup over small alphabets
, 2005
"... Given a dictionary W consisting of n binary strings of length m each, a dquery asks if there exists a string in W within Hamming distance d of a given binary query string q. The problem was posed by Minsky and Papert in 1969 [10] as a challenge to data structure design. Efficient solutions have bee ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Given a dictionary W consisting of n binary strings of length m each, a dquery asks if there exists a string in W within Hamming distance d of a given binary query string q. The problem was posed by Minsky and Papert in 1969 [10] as a challenge to data structure design. Efficient solutions have been developed only for the special case when d = 1 (the 1query problem). We assume the standard RAM model of computation, and consider the case of the problem when alphabet size is arbitrary but finite, and d is small. We preprocess the dictionary, and construct an edgelabelled tree with bounded branching factor, and height. We present an algorithm to answer dictionary lookup within given distance d of a given query string q. The algorithm is efficient when the alphabet size is small, or the dictionary is sparse. In particular, for the dquery problem the algorithm takes time O(m(log 4/3 n − 1) d (log 2 n) d+1). This is an improvement over previously known algorithms for the dquery problem when d> 1. We also generalize the results for the case of the problem when edit distances are used. The algorithm can be modified such that it allows for words of different lengths as well as different lengths of query strings. 1