1,142 research outputs found
On Burst Error Correction and Storage Security of Noisy Data
Secure storage of noisy data for authentication purposes usually involves the
use of error correcting codes. We propose a new model scenario involving burst
errors and present for that several constructions.Comment: to be presented at MTNS 201
Tradeoffs for nearest neighbors on the sphere
We consider tradeoffs between the query and update complexities for the
(approximate) nearest neighbor problem on the sphere, extending the recent
spherical filters to sparse regimes and generalizing the scheme and analysis to
account for different tradeoffs. In a nutshell, for the sparse regime the
tradeoff between the query complexity and update complexity
for data sets of size is given by the following equation in
terms of the approximation factor and the exponents and :
For small , minimizing the time for updates leads to a linear
space complexity at the cost of a query time complexity .
Balancing the query and update costs leads to optimal complexities
, matching bounds from [Andoni-Razenshteyn, 2015] and [Dubiner,
IEEE-TIT'10] and matching the asymptotic complexities of [Andoni-Razenshteyn,
STOC'15] and [Andoni-Indyk-Laarhoven-Razenshteyn-Schmidt, NIPS'15]. A
subpolynomial query time complexity can be achieved at the cost of a
space complexity of the order , matching the bound
of [Andoni-Indyk-Patrascu, FOCS'06] and
[Panigrahy-Talwar-Wieder, FOCS'10] and improving upon results of
[Indyk-Motwani, STOC'98] and [Kushilevitz-Ostrovsky-Rabani, STOC'98].
For large , minimizing the update complexity results in a query complexity
of , improving upon the related exponent for large of
[Kapralov, PODS'15] by a factor , and matching the bound
of [Panigrahy-Talwar-Wieder, FOCS'08]. Balancing the costs leads to optimal
complexities , while a minimum query time complexity can be
achieved with update complexity , improving upon the
previous best exponents of Kapralov by a factor .Comment: 16 pages, 1 table, 2 figures. Mostly subsumed by arXiv:1608.03580
[cs.DS] (along with arXiv:1605.02701 [cs.DS]
Iceberg Hashing: Optimizing Many Hash-Table Criteria at Once
Despite being one of the oldest data structures in computer science, hash
tables continue to be the focus of a great deal of both theoretical and
empirical research. A central reason for this is that many of the fundamental
properties that one desires from a hash table are difficult to achieve
simultaneously; thus many variants offering different trade-offs have been
proposed.
This paper introduces Iceberg hashing, a hash table that simultaneously
offers the strongest known guarantees on a large number of core properties.
Iceberg hashing supports constant-time operations while improving on the state
of the art for space efficiency, cache efficiency, and low failure probability.
Iceberg hashing is also the first hash table to support a load factor of up to
while being stable, meaning that the position where an element is
stored only ever changes when resizes occur. In fact, in the setting where keys
are bits, the space guarantees that Iceberg hashing offers,
namely that it uses at most bits to
store items from a universe , matches a lower bound by Demaine et al.
that applies to any stable hash table.
Iceberg hashing introduces new general-purpose techniques for some of the
most basic aspects of hash-table design. Notably, our indirection-free
technique for dynamic resizing, which we call waterfall addressing, and our
techniques for achieving stability and very-high probability guarantees, can be
applied to any hash table that makes use of the front-yard/backyard paradigm
for hash table design
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