2 research outputs found
Fast Distributed Computation in Dynamic Networks via Random Walks
The paper investigates efficient distributed computation in dynamic networks
in which the network topology changes (arbitrarily) from round to round.
Our first contribution is a rigorous framework for design and analysis of
distributed random walk algorithms in dynamic networks. We then develop a fast
distributed random walk based algorithm that runs in rounds (with high probability), where is the dynamic mixing time
and is the dynamic diameter of the network respectively, and returns a
sample close to a suitably defined stationary distribution of the dynamic
network. We also apply our fast random walk algorithm to devise fast
distributed algorithms for two key problems, namely, information dissemination
and decentralized computation of spectral properties in a dynamic network.
Our next contribution is a fast distributed algorithm for the fundamental
problem of information dissemination (also called as gossip) in a dynamic
network. In gossip, or more generally, -gossip, there are pieces of
information (or tokens) that are initially present in some nodes and the
problem is to disseminate the tokens to all nodes. We present a random-walk
based algorithm that runs in rounds (with high probability). To the best of our knowledge, this is
the first -time fully-distributed token forwarding algorithm that
improves over the previous-best round distributed algorithm [Kuhn et
al., STOC 2010], although in an oblivious adversary model.
Our final contribution is a simple and fast distributed algorithm for
estimating the dynamic mixing time and related spectral properties of the
underlying dynamic network
Distributed Agreement in Dynamic Peer-to-Peer Networks
Motivated by the need for robust and fast distributed computation in highly
dynamic Peer-to-Peer (P2P) networks, we study algorithms for the fundamental
distributed agreement problem. P2P networks are highly dynamic networks that
experience heavy node {\em churn}. Our goal is to design fast algorithms
(running in a small number of rounds) that guarantee, despite high node churn
rate, that almost all nodes reach a stable agreement. Our main contributions
are randomized distributed algorithms that guarantee {\em stable
almost-everywhere agreement} with high probability even under high adversarial
churn in a polylogarithmic number of rounds:
1. An -round ( is the stable network size) randomized
algorithm that achieves almost-everywhere agreement with high probability under
up to {\em linear} churn {\em per round} (i.e., , for some small
constant ), assuming that the churn is controlled by an oblivious
adversary (that has complete knowledge and control of what nodes join and leave
and at what time and has unlimited computational power, but is oblivious to the
random choices made by the algorithm). Our algorithm requires only
polylogarithmic in bits to be processed and sent (per round) by each node.
2. An -round randomized algorithm that achieves
almost-everywhere agreement with high probability under up to churn per round (for some small ), where is the
size of the input value domain, that works even under an adaptive adversary
(that also knows the past random choices made by the algorithm). This algorithm
requires up to polynomial in bits (and up to bits) to be
processed and sent (per round) by each node.Comment: to appear at the Journal of Computer and System Sciences; preliminary
version appeared at SODA 201