Brief Announcement: New Clocks, Fast Line Formation and Self-Replication Population Protocols

Abstract

The model of population protocols is used to study distributed processes based on pairwise interactions between anonymous agents drawn from a large population of size n. The interacting pairs of agents are chosen by the random scheduler and their states are amended by the predefined transition function which governs the considered process. The state space of agents is fixed (constant size) and the size n is not known, i.e., not hard-coded in the transition function. We assume that a population protocol starts in the predefined initial configuration of agents’ states representing the input, and it concludes in an output configuration representing the solution to the considered problem. The time complexity of a protocol refers to the number of interactions required to stabilise this protocol in a final configuration. The parallel time is defined as the time complexity divided by n. In this paper we consider a known variant of the standard population protocol model in which agents can be connected by edges, referred to as the network constructor model. During an interaction between two agents the relevant connecting edge can be formed, maintained or eliminated by the transition function. Since pairs of agents are chosen uniformly at random the status of each edge is updated every Θ( n 2 ) interactions in expectation which coincides with Θ( n ) parallel time. This phenomenon provides a natural lower bound on the time complexity for any non-trivial network construction designed for this variant. This is in contrast with the standard population protocol model in which efficient protocols operate in O ( poly log n ) parallel time. The main focus in this paper is on efficient manipulation of linear structures including formation, self-replication and distribution (including pipelining) of complex information in the adopted model.