326,561 research outputs found
Crux: Locality-Preserving Distributed Services
Distributed systems achieve scalability by distributing load across many
machines, but wide-area deployments can introduce worst-case response latencies
proportional to the network's diameter. Crux is a general framework to build
locality-preserving distributed systems, by transforming an existing scalable
distributed algorithm A into a new locality-preserving algorithm ALP, which
guarantees for any two clients u and v interacting via ALP that their
interactions exhibit worst-case response latencies proportional to the network
latency between u and v. Crux builds on compact-routing theory, but generalizes
these techniques beyond routing applications. Crux provides weak and strong
consistency flavors, and shows latency improvements for localized interactions
in both cases, specifically up to several orders of magnitude for
weakly-consistent Crux (from roughly 900ms to 1ms). We deployed on PlanetLab
locality-preserving versions of a Memcached distributed cache, a Bamboo
distributed hash table, and a Redis publish/subscribe. Our results indicate
that Crux is effective and applicable to a variety of existing distributed
algorithms.Comment: 11 figure
Efficient Construction of Probabilistic Tree Embeddings
In this paper we describe an algorithm that embeds a graph metric
on an undirected weighted graph into a distribution of tree metrics
such that for every pair , and
. Such embeddings have
proved highly useful in designing fast approximation algorithms, as many hard
problems on graphs are easy to solve on tree instances. For a graph with
vertices and edges, our algorithm runs in time with high
probability, which improves the previous upper bound of shown by
Mendel et al.\,in 2009.
The key component of our algorithm is a new approximate single-source
shortest-path algorithm, which implements the priority queue with a new data
structure, the "bucket-tree structure". The algorithm has three properties: it
only requires linear time in the number of edges in the input graph; the
computed distances have a distance preserving property; and when computing the
shortest-paths to the -nearest vertices from the source, it only requires to
visit these vertices and their edge lists. These properties are essential to
guarantee the correctness and the stated time bound.
Using this shortest-path algorithm, we show how to generate an intermediate
structure, the approximate dominance sequences of the input graph, in time, and further propose a simple yet efficient algorithm to converted
this sequence to a tree embedding in time, both with high
probability. Combining the three subroutines gives the stated time bound of the
algorithm.
Then we show that this efficient construction can facilitate some
applications. We proved that FRT trees (the generated tree embedding) are
Ramsey partitions with asymptotically tight bound, so the construction of a
series of distance oracles can be accelerated
Horava-Lifshitz Cosmology: A Review
This article reviews basic construction and cosmological implications of a
power-counting renormalizable theory of gravitation recently proposed by
Horava. We explain that (i) at low energy this theory does not exactly recover
general relativity but instead mimic general relativity plus dark matter; that
(ii) higher spatial curvature terms allow bouncing and cyclic universes as
regular solutions; and that (iii) the anisotropic scaling with the dynamical
critical exponent z=3 solves the horizon problem and leads to scale-invariant
cosmological perturbations even without inflation. We also comment on issues
related to an extra scalar degree of freedom called scalar graviton. In
particular, for spherically-symmetric, static, vacuum configurations we prove
non-perturbative continuity of the lambda->1+0 limit, where lambda is a
parameter in the kinetic action and general relativity has the value lambda=1.
We also derive the condition under which linear instability of the scalar
graviton does not show up.Comment: 28 pages, invited review for CQG; version to be published (v2
Random structures for partially ordered sets
This thesis is presented in two parts. In the first part, we study a family of models
of random partial orders, called classical sequential growth models, introduced by
Rideout and Sorkin as possible models of discrete space-time. We analyse a particular
model, called a random binary growth model, and show that the random partial
order produced by this model almost surely has infinite dimension. We also give
estimates on the size of the largest vertex incomparable to a particular element of
the partial order. We show that there is some positive probability that the random
partial order does not contain a particular subposet. This contrasts with other existing
models of partial orders. We also study "continuum limits" of sequences of
classical sequential growth models. We prove results on the structure of these limits
when they exist, highlighting a deficiency of these models as models of space-time.
In the second part of the thesis, we prove some correlation inequalities for mappings
of rooted trees into complete trees. For T a rooted tree we can define the proportion
of the total number of embeddings of T into a complete binary tree that map the
root of T to the root of the complete binary tree. A theorem of Kubicki, Lehel and
Morayne states that, for two binary trees with one a subposet of the other, this
proportion is larger for the larger tree. They conjecture that the same is true for
two arbitrary trees with one a subposet of the other. We disprove this conjecture
by analysing the asymptotics of this proportion for large complete binary trees.
We show that the theorem of Kubicki, Lehel and Morayne can be thought of as a
correlation inequality which enables us to generalise their result in other directions
POPE: Partial Order Preserving Encoding
Recently there has been much interest in performing search queries over
encrypted data to enable functionality while protecting sensitive data. One
particularly efficient mechanism for executing such queries is order-preserving
encryption/encoding (OPE) which results in ciphertexts that preserve the
relative order of the underlying plaintexts thus allowing range and comparison
queries to be performed directly on ciphertexts. In this paper, we propose an
alternative approach to range queries over encrypted data that is optimized to
support insert-heavy workloads as are common in "big data" applications while
still maintaining search functionality and achieving stronger security.
Specifically, we propose a new primitive called partial order preserving
encoding (POPE) that achieves ideal OPE security with frequency hiding and also
leaves a sizable fraction of the data pairwise incomparable. Using only O(1)
persistent and non-persistent client storage for
, our POPE scheme provides extremely fast batch insertion
consisting of a single round, and efficient search with O(1) amortized cost for
up to search queries. This improved security and
performance makes our scheme better suited for today's insert-heavy databases.Comment: Appears in ACM CCS 2016 Proceeding
Near-Neighbor Preserving Dimension Reduction for Doubling Subsets of l_1
Randomized dimensionality reduction has been recognized as one of the fundamental techniques in handling high-dimensional data. Starting with the celebrated Johnson-Lindenstrauss Lemma, such reductions have been studied in depth for the Euclidean (l_2) metric, but much less for the Manhattan (l_1) metric. Our primary motivation is the approximate nearest neighbor problem in l_1. We exploit its reduction to the decision-with-witness version, called approximate near neighbor, which incurs a roughly logarithmic overhead. In 2007, Indyk and Naor, in the context of approximate nearest neighbors, introduced the notion of nearest neighbor-preserving embeddings. These are randomized embeddings between two metric spaces with guaranteed bounded distortion only for the distances between a query point and a point set. Such embeddings are known to exist for both l_2 and l_1 metrics, as well as for doubling subsets of l_2. The case that remained open were doubling subsets of l_1. In this paper, we propose a dimension reduction by means of a near neighbor-preserving embedding for doubling subsets of l_1. Our approach is to represent the pointset with a carefully chosen covering set, then randomly project the latter. We study two types of covering sets: c-approximate r-nets and randomly shifted grids, and we discuss the tradeoff between them in terms of preprocessing time and target dimension. We employ Cauchy variables: certain concentration bounds derived should be of independent interest
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