5 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
Fast Rendezvous on a Cycle by Agents with Different Speeds
International audienceThe difference between the speed of the actions of different processes is typically considered as an obstacle that makes the achievement of cooperative goals more difficult. In this work, we aim to highlight potential benefits of such asynchrony phenomena to tasks involving symmetry breaking. Specifically, in this paper, identical (except for their speeds) mobile agents are placed at arbitrary locations on a (continuous) cycle of length n and use their speed difference in order to rendezvous fast. We normalize the speed of the slower agent to be 1, and fix the speed of the faster agent to be some c > 1. (An agent does not know whether it is the slower agent or the faster one.) The straightforward distributed-race (DR) algorithm is the one in which both agents simply start walking until rendezvous is achieved. It is easy to show that, in the worst case, the rendezvous time of DR is n/(c − 1). Note that in the interesting case, where c is very close to 1 (e.g., c = 1 + 1/n k ), this bound becomes huge. Our first result is a lower bound showing that, up to a multiplicative factor of 2, this bound is unavoidable, even in a model that allows agents to leave arbitrary marks (the white board model), even assuming sense of direction, and even assuming n and c are known to agents. That is, we show that under such assumptions, the rendezvous time of any algorithm is at least n2(c−1) if c ≤ 3 and slightly larger (specifically, nc+1) if c > 3. We then manage to construct an algorithm that precisely matches the lower bound for the case c ≤ 2, and almost matches it when c > 2. Moreover, our algorithm performs under weaker assumptions than those stated above, as it does not assume sense of direction, and it allows agents to leave only a single mark (a pebble) and only at the place where they start the execution. Finally, we investigate the setting in which no marks can be used at all, and show tight bounds for c ≤ 2, and almost tight bounds for c > 2