361 research outputs found
Dynamics over Signed Networks
A signed network is a network with each link associated with a positive or
negative sign. Models for nodes interacting over such signed networks, where
two different types of interactions take place along the positive and negative
links, respectively, arise from various biological, social, political, and
economic systems. As modifications to the conventional DeGroot dynamics for
positive links, two basic types of negative interactions along negative links,
namely the opposing rule and the repelling rule, have been proposed and studied
in the literature. This paper reviews a few fundamental convergence results for
such dynamics over deterministic or random signed networks under a unified
algebraic-graphical method. We show that a systematic tool of studying node
state evolution over signed networks can be obtained utilizing generalized
Perron-Frobenius theory, graph theory, and elementary algebraic recursions.Comment: In press, SIAM Revie
A Dual Digraph Approach for Leaderless Atomic Broadcast (Extended Version)
Many distributed systems work on a common shared state; in such systems,
distributed agreement is necessary for consistency. With an increasing number
of servers, these systems become more susceptible to single-server failures,
increasing the relevance of fault-tolerance. Atomic broadcast enables
fault-tolerant distributed agreement, yet it is costly to solve. Most practical
algorithms entail linear work per broadcast message. AllConcur -- a leaderless
approach -- reduces the work, by connecting the servers via a sparse resilient
overlay network; yet, this resiliency entails redundancy, limiting the
reduction of work. In this paper, we propose AllConcur+, an atomic broadcast
algorithm that lifts this limitation: During intervals with no failures, it
achieves minimal work by using a redundancy-free overlay network. When failures
do occur, it automatically recovers by switching to a resilient overlay
network. In our performance evaluation of non-failure scenarios, AllConcur+
achieves comparable throughput to AllGather -- a non-fault-tolerant distributed
agreement algorithm -- and outperforms AllConcur, LCR and Libpaxos both in
terms of throughput and latency. Furthermore, our evaluation of failure
scenarios shows that AllConcur+'s expected performance is robust with regard to
occasional failures. Thus, for realistic use cases, leveraging redundancy-free
distributed agreement during intervals with no failures improves performance
significantly.Comment: Overview: 24 pages, 6 sections, 3 appendices, 8 figures, 3 tables.
Modifications from previous version: extended the evaluation of AllConcur+
with a simulation of a multiple datacenters deploymen
Push sum with transmission failures
The push-sum algorithm allows distributed computing of the average on a
directed graph, and is particularly relevant when one is restricted to one-way
and/or asynchronous communications. We investigate its behavior in the presence
of unreliable communication channels where messages can be lost. We show that
exponential convergence still holds and deduce fundamental properties that
implicitly describe the distribution of the final value obtained. We analyze
the error of the final common value we get for the essential case of two nodes,
both theoretically and numerically. We provide performance comparison with a
standard consensus algorithm
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