2 research outputs found
Rendezvous on a Line by Location-Aware Robots Despite the Presence of Byzantine Faults
A set of mobile robots is placed at points of an infinite line. The robots
are equipped with GPS devices and they may communicate their positions on the
line to a central authority. The collection contains an unknown subset of
"spies", i.e., byzantine robots, which are indistinguishable from the
non-faulty ones. The set of the non-faulty robots need to rendezvous in the
shortest possible time in order to perform some task, while the byzantine
robots may try to delay their rendezvous for as long as possible. The problem
facing a central authority is to determine trajectories for all robots so as to
minimize the time until the non-faulty robots have rendezvoused. The
trajectories must be determined without knowledge of which robots are faulty.
Our goal is to minimize the competitive ratio between the time required to
achieve the first rendezvous of the non-faulty robots and the time required for
such a rendezvous to occur under the assumption that the faulty robots are
known at the start. We provide a bounded competitive ratio algorithm, where the
central authority is informed only of the set of initial robot positions,
without knowing which ones or how many of them are faulty. When an upper bound
on the number of byzantine robots is known to the central authority, we provide
algorithms with better competitive ratios. In some instances we are able to
show these algorithms are optimal
Population stability: regulating size in the presence of an adversary
We introduce a new coordination problem in distributed computing that we call
the population stability problem. A system of agents each with limited memory
and communication, as well as the ability to replicate and self-destruct, is
subjected to attacks by a worst-case adversary that can at a bounded rate (1)
delete agents chosen arbitrarily and (2) insert additional agents with
arbitrary initial state into the system. The goal is perpetually to maintain a
population whose size is within a constant factor of the target size . The
problem is inspired by the ability of complex biological systems composed of a
multitude of memory-limited individual cells to maintain a stable population
size in an adverse environment. Such biological mechanisms allow organisms to
heal after trauma or to recover from excessive cell proliferation caused by
inflammation, disease, or normal development.
We present a population stability protocol in a communication model that is a
synchronous variant of the population model of Angluin et al. In each round,
pairs of agents selected at random meet and exchange messages, where at least a
constant fraction of agents is matched in each round. Our protocol uses
three-bit messages and states per agent. We emphasize that
our protocol can handle an adversary that can both insert and delete agents, a
setting in which existing approximate counting techniques do not seem to apply.
The protocol relies on a novel coloring strategy in which the population size
is encoded in the variance of the distribution of colors. Individual agents can
locally obtain a weak estimate of the population size by sampling from the
distribution, and make individual decisions that robustly maintain a stable
global population size