Compacting and grouping mobile agents on dynamic rings

We consider computations by a distributed team of autonomous mobile agents that move on an unoriented dynamic ring network. In particular, we consider 1-interval connected dynamic rings (i.e. at any time, at most one of the edges might be missing). The agents move according to a Look-Compute-Move life cycle, under a synchronous scheduler. The agents may be homogenous (thus identical and monochromatic) or they may be heterogenous (distinct agents have distinct colors from a set of c≥1 colors). For monochromatic agents starting from any dispersed configuration we want the agents to form a compact segment, where agents occupy a continuous part of the ring and no two agents are on the same node – we call this the Compact Configuration Problem. In the case of multiple colors (c>1), agents of the same color are required to occupy continuous segments, such that agents having the same color are all grouped together, while agents of distinct colors are separated. These formation problems are different from the classical and well studied problem of Gathering all agents at a node, since unlike the gathering problem, we do not allow collisions (each node may host at most one agent of a color). We study these two problems and determine the necessary conditions for solving the problems. For all solvable cases, we provide algorithms for both the monochromatic and the colored version of the compact configuration problem, allowing for at most one intersection between the colored segments (which cannot be avoided in a dynamic ring). All our algorithms work even for the simplest model where agents have no persistent memory, no communication capabilities and do not agree on a common orientation. To the best of our knowledge this is the first work on the compaction problem in any type of dynamic network.