Search on a Line by Byzantine Robots

TL;DR

This paper studies fault-tolerant search algorithms for multiple robots on an infinite line, focusing on minimizing search time despite the presence of Byzantine faulty robots that can behave maliciously.

Contribution

It introduces new algorithms for fault-tolerant search with optimality results for certain fault densities, and establishes lower bounds on search time.

Findings

Algorithms achieve optimal search times for specific fault densities.

Lower bounds demonstrate fundamental limits of fault-tolerant search.

Results depend on the ratio of faulty robots to total robots.

Abstract

We consider the problem of fault-tolerant parallel search on an infinite line by $n$ robots. Starting from the origin, the robots are required to find a target at an unknown location. The robots can move with maximum speed $1$ and can communicate in wireless mode among themselves. However, among the $n$ robots, there are $f$ robots that exhibit {\em byzantine faults}. A faulty robot can fail to report the target even after reaching it, or it can make malicious claims about having found the target when in fact it has not. Given the presence of such faulty robots, the search for the target can only be concluded when the non-faulty robots have sufficient verification that the target has been found. We aim to design algorithms that minimize the value of $S_d(n,f)$, the time to find a target at a distance $d$ from the origin by $n$ robots among which $f$ are faulty. We give several different algorithms whose running time depends on the ratio $f/n$, the density of faulty robots, and also prove lower bounds. Our algorithms are optimal for some densities of faulty robots.