5,083 research outputs found
Finite termination of asynchronous iterative algorithms
Includes bibliographical references (p. 17-18).Supported by an AT&T Bell Laboratories GRPW Fellowship. Supported by the NSF. 9300494-DMI Supported by the ARO. DAAL03-92-G-0309Serap A. Savarí, Dimitri P. Bertsekas
Asynchronous iterative computations with Web information retrieval structures: The PageRank case
There are several ideas being used today for Web information retrieval, and
specifically in Web search engines. The PageRank algorithm is one of those that
introduce a content-neutral ranking function over Web pages. This ranking is
applied to the set of pages returned by the Google search engine in response to
posting a search query. PageRank is based in part on two simple common sense
concepts: (i)A page is important if many important pages include links to it.
(ii)A page containing many links has reduced impact on the importance of the
pages it links to. In this paper we focus on asynchronous iterative schemes to
compute PageRank over large sets of Web pages. The elimination of the
synchronizing phases is expected to be advantageous on heterogeneous platforms.
The motivation for a possible move to such large scale distributed platforms
lies in the size of matrices representing Web structure. In orders of
magnitude: pages with nonzero elements and bytes
just to store a small percentage of the Web (the already crawled); distributed
memory machines are necessary for such computations. The present research is
part of our general objective, to explore the potential of asynchronous
computational models as an underlying framework for very large scale
computations over the Grid. The area of ``internet algorithmics'' appears to
offer many occasions for computations of unprecedent dimensionality that would
be good candidates for this framework.Comment: 8 pages to appear at ParCo2005 Conference Proceeding
Byzantine Vector Consensus in Complete Graphs
Consider a network of n processes each of which has a d-dimensional vector of
reals as its input. Each process can communicate directly with all the
processes in the system; thus the communication network is a complete graph.
All the communication channels are reliable and FIFO (first-in-first-out). The
problem of Byzantine vector consensus (BVC) requires agreement on a
d-dimensional vector that is in the convex hull of the d-dimensional input
vectors at the non-faulty processes. We obtain the following results for
Byzantine vector consensus in complete graphs while tolerating up to f
Byzantine failures:
* We prove that in a synchronous system, n >= max(3f+1, (d+1)f+1) is
necessary and sufficient for achieving Byzantine vector consensus.
* In an asynchronous system, it is known that exact consensus is impossible
in presence of faulty processes. For an asynchronous system, we prove that n >=
(d+2)f+1 is necessary and sufficient to achieve approximate Byzantine vector
consensus.
Our sufficiency proofs are constructive. We show sufficiency by providing
explicit algorithms that solve exact BVC in synchronous systems, and
approximate BVC in asynchronous systems.
We also obtain tight bounds on the number of processes for achieving BVC
using algorithms that are restricted to a simpler communication pattern
Real and Complex Monotone Communication Games
Noncooperative game-theoretic tools have been increasingly used to study many
important resource allocation problems in communications, networking, smart
grids, and portfolio optimization. In this paper, we consider a general class
of convex Nash Equilibrium Problems (NEPs), where each player aims to solve an
arbitrary smooth convex optimization problem. Differently from most of current
works, we do not assume any specific structure for the players' problems, and
we allow the optimization variables of the players to be matrices in the
complex domain. Our main contribution is the design of a novel class of
distributed (asynchronous) best-response- algorithms suitable for solving the
proposed NEPs, even in the presence of multiple solutions. The new methods,
whose convergence analysis is based on Variational Inequality (VI) techniques,
can select, among all the equilibria of a game, those that optimize a given
performance criterion, at the cost of limited signaling among the players. This
is a major departure from existing best-response algorithms, whose convergence
conditions imply the uniqueness of the NE. Some of our results hinge on the use
of VI problems directly in the complex domain; the study of these new kind of
VIs also represents a noteworthy innovative contribution. We then apply the
developed methods to solve some new generalizations of SISO and MIMO games in
cognitive radios and femtocell systems, showing a considerable performance
improvement over classical pure noncooperative schemes.Comment: to appear on IEEE Transactions in Information Theor
Iterative Approximate Consensus in the presence of Byzantine Link Failures
This paper explores the problem of reaching approximate consensus in
synchronous point-to-point networks, where each directed link of the underlying
communication graph represents a communication channel between a pair of nodes.
We adopt the transient Byzantine link failure model [15, 16], where an
omniscient adversary controls a subset of the directed communication links, but
the nodes are assumed to be fault-free.
Recent work has addressed the problem of reaching approximate consen- sus in
incomplete graphs with Byzantine nodes using a restricted class of iterative
algorithms that maintain only a small amount of memory across iterations [22,
21, 23, 12]. However, to the best of our knowledge, we are the first to
consider approximate consensus in the presence of Byzan- tine links. We extend
our past work that provided exact characterization of graphs in which the
iterative approximate consensus problem in the presence of Byzantine node
failures is solvable [22, 21]. In particular, we prove a tight necessary and
sufficient condition on the underlying com- munication graph for the existence
of iterative approximate consensus algorithms under transient Byzantine link
model. The condition answers (part of) the open problem stated in [16].Comment: arXiv admin note: text overlap with arXiv:1202.609
Solving the At-Most-Once Problem with Nearly Optimal Effectiveness
We present and analyze a wait-free deterministic algorithm for solving the
at-most-once problem: how m shared-memory fail-prone processes perform
asynchronously n jobs at most once. Our algorithmic strategy provides for the
first time nearly optimal effectiveness, which is a measure that expresses the
total number of jobs completed in the worst case. The effectiveness of our
algorithm equals n-2m+2. This is up to an additive factor of m close to the
known effectiveness upper bound n-m+1 over all possible algorithms and improves
on the previously best known deterministic solutions that have effectiveness
only n-log m o(n). We also present an iterative version of our algorithm that
for any is both
effectiveness-optimal and work-optimal, for any constant . We
then employ this algorithm to provide a new algorithmic solution for the
Write-All problem which is work optimal for any
.Comment: Updated Version. A Brief Announcement was published in PODC 2011. An
Extended Abstract was published in the proceeding of ICDCN 2012. A full
version was published in Theoretical Computer Science, Volume 496, 22 July
2013, Pages 69 - 8
- …