Paper in proceedings, 2016

In multi-agent rendezvous it is naturally assumed that agents have a maximum speed of movement. In the absence of any distributed control issues, this imposes a lower bound on the time to rendezvous, for idealised point agents, proportional to the diameter of a configuration. Assuming bounded visibility, we consider Ω(n2 log n) points distributed independently and uniformly at random in a disc of radius n, so that the visibility graph is asymptotically almost surely (a.a.s.) connected. We allow three types of possible interaction between neighbors, which we term signalling, sweeping and tracking. Assuming any such interaction can be executed without significant delay, and assuming each point can generate random bits and has unlimited memory, we describe a randomized algorithm which a.a.s. runs in time O(n), hence in time proportional to the diameter, provided the number of points is o(n3). Several questions are posed for future work.

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Art. no. a2-

Information and Communication Technology

Computer and Information Science

Discrete Mathematics

Basic sciences

10.1145/2833312.2833457

978-1-4503-4032-8