1,063 research outputs found
Distributed Machine Learning via Sufficient Factor Broadcasting
Matrix-parametrized models, including multiclass logistic regression and
sparse coding, are used in machine learning (ML) applications ranging from
computer vision to computational biology. When these models are applied to
large-scale ML problems starting at millions of samples and tens of thousands
of classes, their parameter matrix can grow at an unexpected rate, resulting in
high parameter synchronization costs that greatly slow down distributed
learning. To address this issue, we propose a Sufficient Factor Broadcasting
(SFB) computation model for efficient distributed learning of a large family of
matrix-parameterized models, which share the following property: the parameter
update computed on each data sample is a rank-1 matrix, i.e., the outer product
of two "sufficient factors" (SFs). By broadcasting the SFs among worker
machines and reconstructing the update matrices locally at each worker, SFB
improves communication efficiency --- communication costs are linear in the
parameter matrix's dimensions, rather than quadratic --- without affecting
computational correctness. We present a theoretical convergence analysis of
SFB, and empirically corroborate its efficiency on four different
matrix-parametrized ML models
Fast Routing Table Construction Using Small Messages
We describe a distributed randomized algorithm computing approximate
distances and routes that approximate shortest paths. Let n denote the number
of nodes in the graph, and let HD denote the hop diameter of the graph, i.e.,
the diameter of the graph when all edges are considered to have unit weight.
Given 0 < eps <= 1/2, our algorithm runs in weak-O(n^(1/2 + eps) + HD)
communication rounds using messages of O(log n) bits and guarantees a stretch
of O(eps^(-1) log eps^(-1)) with high probability. This is the first
distributed algorithm approximating weighted shortest paths that uses small
messages and runs in weak-o(n) time (in graphs where HD in weak-o(n)). The time
complexity nearly matches the lower bounds of weak-Omega(sqrt(n) + HD) in the
small-messages model that hold for stateless routing (where routing decisions
do not depend on the traversed path) as well as approximation of the weigthed
diameter. Our scheme replaces the original identifiers of the nodes by labels
of size O(log eps^(-1) log n). We show that no algorithm that keeps the
original identifiers and runs for weak-o(n) rounds can achieve a
polylogarithmic approximation ratio.
Variations of our techniques yield a number of fast distributed approximation
algorithms solving related problems using small messages. Specifically, we
present algorithms that run in weak-O(n^(1/2 + eps) + HD) rounds for a given 0
< eps <= 1/2, and solve, with high probability, the following problems:
- O(eps^(-1))-approximation for the Generalized Steiner Forest (the running
time in this case has an additive weak-O(t^(1 + 2eps)) term, where t is the
number of terminals);
- O(eps^(-2))-approximation of weighted distances, using node labels of size
O(eps^(-1) log n) and weak-O(n^(eps)) bits of memory per node;
- O(eps^(-1))-approximation of the weighted diameter;
- O(eps^(-3))-approximate shortest paths using the labels 1,...,n.Comment: 40 pages, 2 figures, extended abstract submitted to STOC'1
DNA electrophoresis studied with the cage model
The cage model for polymer reptation, proposed by Evans and Edwards, and its
recent extension to model DNA electrophoresis, are studied by numerically exact
computation of the drift velocities for polymers with a length L of up to 15
monomers. The computations show the Nernst-Einstein regime (v ~ E) followed by
a regime where the velocity decreases exponentially with the applied electric
field strength. In agreement with de Gennes' reptation arguments, we find that
asymptotically for large polymers the diffusion coefficient D decreases
quadratically with polymer length; for the cage model, the proportionality
coefficient is DL^2=0.175(2). Additionally we find that the leading correction
term for finite polymer lengths scales as N^{-1/2}, where N=L-1 is the number
of bonds.Comment: LaTeX (cjour.cls), 15 pages, 6 figures, added correctness proof of
kink representation approac
Parallel Algorithms for Geometric Graph Problems
We give algorithms for geometric graph problems in the modern parallel models
inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem
over a set of points in the two-dimensional space, our algorithm computes a
-approximate MST. Our algorithms work in a constant number of
rounds of communication, while using total space and communication proportional
to the size of the data (linear space and near linear time algorithms). In
contrast, for general graphs, achieving the same result for MST (or even
connectivity) remains a challenging open problem, despite drawing significant
attention in recent years.
We develop a general algorithmic framework that, besides MST, also applies to
Earth-Mover Distance (EMD) and the transportation cost problem. Our algorithmic
framework has implications beyond the MapReduce model. For example it yields a
new algorithm for computing EMD cost in the plane in near-linear time,
. We note that while recently Sharathkumar and Agarwal
developed a near-linear time algorithm for -approximating EMD,
our algorithm is fundamentally different, and, for example, also solves the
transportation (cost) problem, raised as an open question in their work.
Furthermore, our algorithm immediately gives a -approximation
algorithm with space in the streaming-with-sorting model with
passes. As such, it is tempting to conjecture that the
parallel models may also constitute a concrete playground in the quest for
efficient algorithms for EMD (and other similar problems) in the vanilla
streaming model, a well-known open problem
Using parallel pivot vs. clustering-based techniques for web engines
Web Engines are a useful tool for searching information in the Web. But a great part of this
information is non-textual and for that case a metric space is used. A metric space is a set where a
notion of distance (called a metric) between elements of the set is defined. In this paper we present
an efficient parallelization of a pivot-based method devised for this purpose which is called the
Sparse Spatial Selection (SSS) strategy and we compare it with a clustering-based method, a
parallel implementation of the Spatial Approximation Tree (SAT). We show that SAT compares
favourably against the pivot data structures SSS. The experimental results were obtained on a highperformance
cluster and using several metric spaces, that shows load balance parallel strategies
for the SAT. The implementations are built upon the BSP parallel computing model, which shows
efficient performance for this application domain and allows a precise evaluation of algorithms.VIII Workshop de Procesamiento Distribuido y ParaleloRed de Universidades con Carreras en Informática (RedUNCI
Using parallel pivot vs. clustering-based techniques for web engines
Web Engines are a useful tool for searching information in the Web. But a great part of this
information is non-textual and for that case a metric space is used. A metric space is a set where a
notion of distance (called a metric) between elements of the set is defined. In this paper we present
an efficient parallelization of a pivot-based method devised for this purpose which is called the
Sparse Spatial Selection (SSS) strategy and we compare it with a clustering-based method, a
parallel implementation of the Spatial Approximation Tree (SAT). We show that SAT compares
favourably against the pivot data structures SSS. The experimental results were obtained on a highperformance
cluster and using several metric spaces, that shows load balance parallel strategies
for the SAT. The implementations are built upon the BSP parallel computing model, which shows
efficient performance for this application domain and allows a precise evaluation of algorithms.VIII Workshop de Procesamiento Distribuido y ParaleloRed de Universidades con Carreras en Informática (RedUNCI
Scalable Facility Location for Massive Graphs on Pregel-like Systems
We propose a new scalable algorithm for facility location. Facility location
is a classic problem, where the goal is to select a subset of facilities to
open, from a set of candidate facilities F , in order to serve a set of clients
C. The objective is to minimize the total cost of opening facilities plus the
cost of serving each client from the facility it is assigned to. In this work,
we are interested in the graph setting, where the cost of serving a client from
a facility is represented by the shortest-path distance on the graph. This
setting allows to model natural problems arising in the Web and in social media
applications. It also allows to leverage the inherent sparsity of such graphs,
as the input is much smaller than the full pairwise distances between all
vertices.
To obtain truly scalable performance, we design a parallel algorithm that
operates on clusters of shared-nothing machines. In particular, we target
modern Pregel-like architectures, and we implement our algorithm on Apache
Giraph. Our solution makes use of a recent result to build sketches for massive
graphs, and of a fast parallel algorithm to find maximal independent sets, as
building blocks. In so doing, we show how these problems can be solved on a
Pregel-like architecture, and we investigate the properties of these
algorithms. Extensive experimental results show that our algorithm scales
gracefully to graphs with billions of edges, while obtaining values of the
objective function that are competitive with a state-of-the-art sequential
algorithm
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