Different local controls for graph relabeling systems

Abstract

We are interested in models to encode and to prove decentralized and distributed computations on graphs. In this paper we define and compare six models of graph relabeling systems. These systems do not change the underlying structure of the graph on which they work, but only the labeling of its components (edges or vertices). Each relabeling step is fully determined by the knowledge of a fixed-size subgraph, the local context of the relabeled occurrence. The families studied are based on the relabeling of partial or induced subgraphs and we use two kinds of mechanisms to control the applicability of rules locally: a priority relation on the set of rules or a set of forbidden contexts associated with each rule. We show that these two basic (i.e., without local control) families of graph relabeling systems are distinct, but whenever we consider the local controls of the relabeling, the four families so obtained are equivalent.