11,421 research outputs found
Lower Bounds for Oblivious Near-Neighbor Search
We prove an lower bound on the dynamic
cell-probe complexity of statistically
approximate-near-neighbor search () over the -dimensional
Hamming cube. For the natural setting of , our result
implies an lower bound, which is a quadratic
improvement over the highest (non-oblivious) cell-probe lower bound for
. This is the first super-logarithmic
lower bound for against general (non black-box) data structures.
We also show that any oblivious data structure for
decomposable search problems (like ) can be obliviously dynamized
with overhead in update and query time, strengthening a classic
result of Bentley and Saxe (Algorithmica, 1980).Comment: 28 page
Connectivity Oracles for Graphs Subject to Vertex Failures
We introduce new data structures for answering connectivity queries in graphs
subject to batched vertex failures. A deterministic structure processes a batch
of failed vertices in time and thereafter
answers connectivity queries in time. It occupies space . We develop a randomized Monte Carlo version of our data structure
with update time , query time , and space
for any failure bound . This is the first connectivity oracle for
general graphs that can efficiently deal with an unbounded number of vertex
failures.
We also develop a more efficient Monte Carlo edge-failure connectivity
oracle. Using space , edge failures are processed in time and thereafter, connectivity queries are answered in
time, which are correct w.h.p.
Our data structures are based on a new decomposition theorem for an
undirected graph , which is of independent interest. It states that
for any terminal set we can remove a set of
vertices such that the remaining graph contains a Steiner forest for with
maximum degree
Fundamental Limits on Data Acquisition: Trade-offs between Sample Complexity and Query Difficulty
We consider query-based data acquisition and the corresponding information
recovery problem, where the goal is to recover binary variables
(information bits) from parity measurements of those variables. The queries and
the corresponding parity measurements are designed using the encoding rule of
Fountain codes. By using Fountain codes, we can design potentially limitless
number of queries, and corresponding parity measurements, and guarantee that
the original information bits can be recovered with high probability from
any sufficiently large set of measurements of size . In the query design,
the average number of information bits that is associated with one parity
measurement is called query difficulty () and the minimum number of
measurements required to recover the information bits for a fixed
is called sample complexity (). We analyze the fundamental trade-offs
between the query difficulty and the sample complexity, and show that the
sample complexity of for some constant
is necessary and sufficient to recover information bits with high
probability as
Towards a compact representation of temporal rasters
Big research efforts have been devoted to efficiently manage spatio-temporal
data. However, most works focused on vectorial data, and much less, on raster
data. This work presents a new representation for raster data that evolve along
time named Temporal k^2 raster. It faces the two main issues that arise when
dealing with spatio-temporal data: the space consumption and the query response
times. It extends a compact data structure for raster data in order to manage
time and thus, it is possible to query it directly in compressed form, instead
of the classical approach that requires a complete decompression before any
manipulation. In addition, in the same compressed space, the new data structure
includes two indexes: a spatial index and an index on the values of the cells,
thus becoming a self-index for raster data.Comment: This research has received funding from the European Union's Horizon
2020 research and innovation programme under the Marie Sklodowska-Curie
Actions H2020-MSCA-RISE-2015 BIRDS GA No. 690941. Published in SPIRE 201
Crossing the Logarithmic Barrier for Dynamic Boolean Data Structure Lower Bounds
This paper proves the first super-logarithmic lower bounds on the cell probe
complexity of dynamic boolean (a.k.a. decision) data structure problems, a
long-standing milestone in data structure lower bounds.
We introduce a new method for proving dynamic cell probe lower bounds and use
it to prove a lower bound on the operational
time of a wide range of boolean data structure problems, most notably, on the
query time of dynamic range counting over ([Pat07]). Proving an
lower bound for this problem was explicitly posed as one of
five important open problems in the late Mihai P\v{a}tra\c{s}cu's obituary
[Tho13]. This result also implies the first lower bound for the
classical 2D range counting problem, one of the most fundamental data structure
problems in computational geometry and spatial databases. We derive similar
lower bounds for boolean versions of dynamic polynomial evaluation and 2D
rectangle stabbing, and for the (non-boolean) problems of range selection and
range median.
Our technical centerpiece is a new way of "weakly" simulating dynamic data
structures using efficient one-way communication protocols with small advantage
over random guessing. This simulation involves a surprising excursion to
low-degree (Chebychev) polynomials which may be of independent interest, and
offers an entirely new algorithmic angle on the "cell sampling" method of
Panigrahy et al. [PTW10]
LRM-Trees: Compressed Indices, Adaptive Sorting, and Compressed Permutations
LRM-Trees are an elegant way to partition a sequence of values into sorted
consecutive blocks, and to express the relative position of the first element
of each block within a previous block. They were used to encode ordinal trees
and to index integer arrays in order to support range minimum queries on them.
We describe how they yield many other convenient results in a variety of areas,
from data structures to algorithms: some compressed succinct indices for range
minimum queries; a new adaptive sorting algorithm; and a compressed succinct
data structure for permutations supporting direct and indirect application in
time all the shortest as the permutation is compressible.Comment: 13 pages, 1 figur
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