Backyard Cuckoo Hashing: Constant Worst-Case Operations with a Succinct Representation
Speaker: Moni Naor , Weizmann InstituteContact:
Date: December 15 2009
Time: 4:15PM to 5:15PM
Host: Scott Aaronson, TOC, CSAIL
Be, 3-6098, email@example.comRelevant URL:
The performance of a dynamic dictionary is measured mainly by its update
time, lookup time, and space consumption. Although the first analysis of a
dynamic dictionary dates back more than 45 years ago (when Knuth analyzed
linear probing in 1963), the trade-off between these aspects of performance is still not completely understood.
In this talk I will focus on a recent line of work with the goal of
achieving the best possible performance guarantees simultaneously.
In particular, the following constructions will be described:
-- A de-amortization of cuckoo hashing that stores n elements using
roughly 2n memory words, and guarantees constant-time time operations
in the worst case with high probability, for any sequence of polynomially many operations.
-- The first dynamic dictionary that enjoys the best of both worlds: a
two-level variant of cuckoo hashing that stores n elements using
(1+o(1))n memory words, and guarantees constant-time operations in
the worst case as above. The construction is based on augmenting
cuckoo hashing with a "backyard" that handles a large fraction of the
elements, together with a de-amortized perfect hashing scheme for
eliminating the dependency on bin sizes.
--- A variant of the previous construction that stores n elements using
only (1+o(1))B bits, where B is the information-theoretic lower bound
for representing a (static) set of size n taken from a universe of size u,
and guarantees constant-time operations in the worst case with
high probability, as before. This problem was open even in the
Joint work with Yuriy Arbitman and Gil Segev.
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