“Robots in Space” Multiagent Problem: Complexity, Information and Cryptographic Aspects

We study a multiagent algorithmic problem that we call Robot in Space (RinS): There are $n\geq 2$ autonomous robots, that need to agree without outside interference on distribution of shelters, so that straight pathes to the shelters will not intersect. The problem is closely related to the assignment problem in Graph Theory, to the convex hull problem in Combinatorial Geometry, or to the path-planning problem in Artificial Intelligence. Our algorithm grew up from a local search solution of the problem suggested by E. W. Dijkstra. We present a multiagent anonymous and scalable algorithm (protocol) solving the problem, give an upper bound for the algorithm, prove (manually) its correctness, and examine two communication aspects of the RinS problem — the informational and cryptographic. We proved that (1) there is no protocol that solves the RinS, which transfers a bounded number of bits, and (2) suggested the protocol that allows robots to check whether their paths intersect, without revealing additional information about their relative positions (with respect to shelters). The present paper continues the research presented in Mars Robot Puzzle (a Multiagent Approach to the Dijkstra Problem) (by E. V. Bodin, N. O. Garanina, and N. V. Shilov), published in Modeling and analysis of information systems, 18(2), 2011.