Maximum Matching for Anonymous Trees with Constant Space per Process

We give a silent self-stabilizing protocol for computing a maximum matching in an anonymous network with a tree topology. The round complexity of our protocol is Opdiamq, where diam is the diameter of the network, and the step complexity is Opn diamq, where n is the number of processes in the network. The working space complexity is Op1q per process, although the output necessarily takes Oplog δq space per process, where δ is the degree of that process. To implement parent pointers in constant space, regardless of degree, we use the cyclic Abelian group Z7. 1998 ACM Subject Classification C.2.4 [Computer-Communication Networks] Distributed Systems, F.2.2 [Analysis of Algorithms and Problem Complexity] Nonnumerical Algorithms and Problems, G.2.2 [Discrete Mathematics] Graph Algorithms