Byzantine fault-tolerant protocols for (n,f)-evacuation from a circle

Abstract

In this work, we address the problem of $(n,f)$-evacuation on a circle, which involves evacuating n robots, with f of them being faulty, from a hidden exit located on the perimeter of a unit radius circle. The robots commence at the center of the circle and possess a speed of 1.

We introduce algorithms for both the Wireless and Face-to-Face communication models tolerating f Byzantine faults. We set constraints on f and we analyze the time requirements of these algorithms and we establish upper bounds on their performance.

We propose an algorithm for the Wireless communication model, proving the following upper bound$E(n,f)\le 1+(f+1)\cdot \frac{2\pi }{n}+\max \left\{G_e\right(k^{⁎}),H_e(k^{⁎}\left)\right\}$ where $G_e\left(k^{⁎}\right)$ and $H_e\left(k^{⁎}\right)$ is the time needed to evacuate two crucial groups of robots, during the execution of our algorithm.

For the Face-to-Face communication model we propose an algorithm and we prove an upper bound of$E(n,f)\le 3+(f+1)\cdot \frac{2\pi }{n}+\underset{2\le k\le n}{\max }\left\{2\right(k-1)\cdot \sin (\frac{f-k+2}{k-1}\cdot \frac{\pi }{n})\}$ where k is the number of conflicting accounts of the exit position.