Rendezvous on a Line by Location-Aware Robots Despite the Presence of Byzantine Faults

TL;DR

This paper studies how to coordinate mobile robots on a line to rendezvous quickly despite some being malicious Byzantine robots, proposing algorithms with optimal or near-optimal performance guarantees.

Contribution

It introduces algorithms for robot rendezvous on a line that are robust against Byzantine faults, achieving bounded competitive ratios without prior fault knowledge.

Findings

Algorithms with bounded competitive ratios for rendezvous despite Byzantine faults.

Improved algorithms when an upper bound on Byzantine robots is known.

Some algorithms are proven to be optimal in certain cases.

Abstract

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.