TY - GEN
T1 - Polynomial hash functions are reliable
AU - Dietzfelbinger, M.
AU - Gil, J.
AU - Matias, Y.
AU - Pippenger, N.
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1992.
PY - 1992
Y1 - 1992
N2 - Polynomial hash functions are well studied and widely used in various applications. They have gained popularity because of certain performances they exhibit. It has been shown that even linear hash functions are expected to have such performances. However, quite often we would like the hash functions to be reliable, meaning that they perform well with high probability; for some certain important properties even higher degree polynomials were not known to be reliable. We show thal, for certain important properties linear hash functions are not reliable. We give indication that quadratic hash functions might not be reliable. On the positive side, we prove that cubic hash functions are reliable. In a more general setting, we show that higher degree of the polynomial hash functions translates into higher reliability. We also introduce a new class of hash functions, which enables to reduce the universe size in an efficient and simple manner. The reliability results and the new class of hash functions are used for some fimdamental applications: improved and simplified reliable algorithms for perfect hash functions and real-time dictionaries, which use significantly less random bits, and tighter upper bound for the program size of perfect hash functions.
AB - Polynomial hash functions are well studied and widely used in various applications. They have gained popularity because of certain performances they exhibit. It has been shown that even linear hash functions are expected to have such performances. However, quite often we would like the hash functions to be reliable, meaning that they perform well with high probability; for some certain important properties even higher degree polynomials were not known to be reliable. We show thal, for certain important properties linear hash functions are not reliable. We give indication that quadratic hash functions might not be reliable. On the positive side, we prove that cubic hash functions are reliable. In a more general setting, we show that higher degree of the polynomial hash functions translates into higher reliability. We also introduce a new class of hash functions, which enables to reduce the universe size in an efficient and simple manner. The reliability results and the new class of hash functions are used for some fimdamental applications: improved and simplified reliable algorithms for perfect hash functions and real-time dictionaries, which use significantly less random bits, and tighter upper bound for the program size of perfect hash functions.
UR - http://www.scopus.com/inward/record.url?scp=84860839700&partnerID=8YFLogxK
U2 - 10.1007/3-540-55719-9_77
DO - 10.1007/3-540-55719-9_77
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AN - SCOPUS:84860839700
SN - 9783540557197
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 235
EP - 246
BT - Automata, Languages and Programming - 19th International Colloquium, Proceedings
A2 - Kuich, Werner
PB - Springer Verlag
T2 - 19th International Colloquium on Automata, Languages, and Programming, ICALP 1992
Y2 - 13 July 1992 through 17 July 1992
ER -