Keywords and Synonyms
Static membership ; Approximate membership
Problem Definition
The Problem and the Model
A static data structure problem consists of a set of data D, a set of queries Q, a set of answers A, and a function \( { f \colon D \times Q \rightarrow A } \). The goal is to store the data succinctly so that any query can be answered with only a few probes to the data structure. Static membership is a well-studied problem in data structure design [1,4,7,8,12,13,16].
Definition 1 (Static Membership)
In the static membership problem, one is given a subset S of at most n keys from a universe \( { U=\{1,2,\ldots,m\} } \). The task is to store S so that queries of the form “Is u in S?” can be answered by making few accesses to the memory.
A natural and general model for studying any data structure problem is the cell probe model proposed by Yao [16].
Definition 2 (Cell Probe Model)
An \( { (s,w,t) } \) cell probe scheme for a static data structure problem \( { f \colon D \times Q...
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Brodnik, A., Munro, J.I.: Membership in constant time and minimum space. In: Lecture Notes in Computer Science, vol. 855, pp. 72–81, Springer, Berlin (1994). Final version: Membership in Constant Time and Almost‐Minimum Space. SIAM J. Comput. 28(5), 1627–1640 (1999)
Buhrman, H., Miltersen, P.B., Radhakrishnan, J., Venkatesh, S.: Are bitvectors optimal? SIAM J. Comput. 31(6), 1723–1744 (2002)
Dyachkov, A.G., Rykov, V.V.: Bounds on the length of disjunctive codes. Problemy Peredachi Informatsii 18(3), 7–13 (1982)
Elias, P., Flower, R.A.: The complexity of some simple retrieval problems. J. Assoc. Comput. Mach. 22, 367–379 (1975)
Erdös, P., Frankl, P., Füredi, Z.: Families of finite sets in which no set is covered by the union of r others. Isr. J. Math. 51, 79–89 (1985)
Fiat, A., Naor, M.: Implicit O(1) probe search. SIAM J. Comput. 22, 1–10 (1993)
Fiat, A., Naor, M., Schmidt, J.P., Siegel, A.: Non‐oblivious hashing. J. Assoc. Comput. Mach. 31, 764–782 (1992)
Fredman, M.L., Komlós, J., Szemerédi, E.: Storing a sparse table with \( { {O(1)} } \) worst case access time. J. Assoc. Comput. Mach. 31(3), 538–544 (1984)
Füredi, Z.: On r-cover-free families. J. Comb. Theory, Series A 73, 172–173 (1996)
Katz, J., Trevisan, L.: On the efficiency of local decoding procedures for error‐correcting codes. In: Proceedings of STOC'00, pp. 80–86
Miltersen, P.B., Nisan, N., Safra, S., Wigderson, A.: On data structures and asymmetric communication complexity. J. Comput. Syst. Sci. 57, 37–49 (1998)
Minsky, M., Papert, S.: Perceptrons. MIT Press, Cambridge (1969)
Pagh, R.: Low redundancy in static dictionaries with O(1) lookup time. In: Proceedings of ICALP '99. LNCS, vol. 1644, pp. 595–604. Springer, Berlin (1999)
Ruszinkó, M. On the upper bound of the size of r-cover-free families. J. Comb. Theory, Ser. A 66, 302–310 (1984)
Ta-Shma, A.: Explicit one-probe storing schemes using universal extractors. Inf. Proc. Lett. 83(5), 267–274 (2002)
Yao, A.C.C.: Should tables be sorted? J. Assoc. Comput. Mach. 28(3), 615–628 (1981)
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Srinivasan, V. (2008). Approximate Dictionaries. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_16
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