Self-Stabilizing Mutual Exclusion on Directed Graphs

This paper investigates the complexity of self-stabilizing mutual exclusion protocols for distributed systems, where processors communicate through shared memory according to a strongly connected directed communication graph. Tchuente's approach of covering a network with one directed cycle is taken as point of departure. This protocol requires O(n 2n) states per processor together with some preprocessing. By coalescing states a protocol requiring only O(n 2) states per processor|still requiring preprocessing|is derived. Finally two protocols based on spanning trees are considered. Combining these protocols with a self-stabilizing spanning tree protocol yields two O(n 3 m)|where m is the maximal degree of a processor|states per processor protocols that require knowledge of processor identities. This report concludes with a full proof of the coalesced states protocol in Lamport's Temporal Logic of Actions. Note: The last three authors were partially supported by the Dutch foundation for scientiic research (NWO) through NFI Project ALADDIN, under contract number NF 62-376