Abstract:
This paper considers the problem of
Byzantine dispersion and extends previous work along
several parameters. The problem of Byzantine dispersion asks: given n robots, up to f of which are Byzantine,
initially placed arbitrarily on an n node anonymous
graph, design a terminating algorithm to be run by the
robots such that they eventually reach a configuration
where each node has at most one non-Byzantine robot
on it.
Previous work solved this problem for rings and
tolerated up to n − 1 Byzantine robots. In this paper,
we investigate the problem on more general graphs.
We first develop an algorithm that tolerates up to
n − 1 Byzantine robots and works for a more general
class of graphs. We then develop an algorithm that
works for any graph but tolerates a lesser number of
Byzantine robots. We subsequently turn our focus to
the strength of the Byzantine robots. Previous work
considers only “weak” Byzantine robots that cannot
fake their IDs. We develop an algorithm that solves
the problem when Byzantine robots are not weak and
can fake IDs. Finally, we study the situation where the
number of the robots is not n but some k. We show
that in such a scenario, the number of Byzantine robots
that can be tolerated is severely restricted. Specifically,
we show that it is impossible to deterministically solve
Byzantine dispersion when k/n > (k − f)/n.
