2 research outputs found
Consensus in Networks Prone to Link Failures
We consider deterministic distributed algorithms solving Consensus in
synchronous networks of arbitrary topologies. Links are prone to failures.
Agreement is understood as holding in each connected component of a network
obtained by removing faulty links. We introduce the concept of stretch, which
is a function of the number of connected components of a network and their
respective diameters. Fast and early-stopping algorithms solving Consensus are
defined by referring to stretch resulting in removing faulty links. We develop
algorithms that rely only on nodes knowing their own names and the ability to
associate communication with local ports. A network has nodes and it starts
with functional links. We give a general algorithm operating in time
that uses messages of bits. If we additionally restrict executions
to be subject to a bound on stretch, then there is a fast algorithm
solving Consensus in time using messages of bits. Let
be an unknown stretch occurring in an execution; we give an algorithm
working in time and using messages of bits. We
show that Consensus can be solved in the optimal time, but at the
cost of increasing message size to . We also demonstrate how to
solve Consensus by an algorithm that uses only non-faulty links and
works in time , while nodes start with their ports mapped to neighbors
and messages carry bits. We prove lower bounds on performance of
Consensus solutions that refer to parameters of evolving network topologies and
the knowledge available to nodes