11,031 research outputs found
Effectiveness of landmark analysis for establishing locality in p2p networks
Locality to other nodes on a peer-to-peer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multi-dimensional feature vector. Each peer node uses the feature vector to generate a unique scalar index which is correlated to its topological locality. A popular dimensionality reduction technique is the space filling Hilbert’s curve, as it possesses good locality
preserving properties. However, there exists little comparison between Hilbert’s curve and other techniques for dimensionality reduction. This work carries out a quantitative analysis of their properties. Linear and non-linear techniques for scaling the landmark vectors to a single dimension are investigated. Hilbert’s curve, Sammon’s mapping and Principal Component Analysis
have been used to generate a 1d space with locality preserving properties. This work provides empirical evidence to support the use of Hilbert’s curve in the context of locality preservation when generating peer identifiers by means of landmark vector analysis. A comparative analysis is carried out with an artificial 2d network model and with a realistic network topology model
with a typical power-law distribution of node connectivity in the Internet. Nearest neighbour analysis confirms Hilbert’s curve to be very effective in both artificial and realistic network topologies. Nevertheless, the results in the realistic network model show that there is scope for improvements and better techniques to preserve locality information are required
Fault-tolerant routing in peer-to-peer systems
We consider the problem of designing an overlay network and routing mechanism
that permits finding resources efficiently in a peer-to-peer system. We argue
that many existing approaches to this problem can be modeled as the
construction of a random graph embedded in a metric space whose points
represent resource identifiers, where the probability of a connection between
two nodes depends only on the distance between them in the metric space. We
study the performance of a peer-to-peer system where nodes are embedded at grid
points in a simple metric space: a one-dimensional real line. We prove upper
and lower bounds on the message complexity of locating particular resources in
such a system, under a variety of assumptions about failures of either nodes or
the connections between them. Our lower bounds in particular show that the use
of inverse power-law distributions in routing, as suggested by Kleinberg
(1999), is close to optimal. We also give efficient heuristics to dynamically
maintain such a system as new nodes arrive and old nodes depart. Finally, we
give experimental results that suggest promising directions for future work.Comment: Full version of PODC 2002 paper. New version corrects missing
conditioning in Lemma 9 and some related details in the proof of Theorem 10,
with no changes to main result
POD model order reduction with space-adapted snapshots for incompressible flows
We consider model order reduction based on proper orthogonal decomposition
(POD) for unsteady incompressible Navier-Stokes problems, assuming that the
snapshots are given by spatially adapted finite element solutions. We propose
two approaches of deriving stable POD-Galerkin reduced-order models for this
context. In the first approach, the pressure term and the continuity equation
are eliminated by imposing a weak incompressibility constraint with respect to
a pressure reference space. In the second approach, we derive an inf-sup stable
velocity-pressure reduced-order model by enriching the velocity reduced space
with supremizers computed on a velocity reference space. For problems with
inhomogeneous Dirichlet conditions, we show how suitable lifting functions can
be obtained from standard adaptive finite element computations. We provide a
numerical comparison of the considered methods for a regularized lid-driven
cavity problem
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