Eeciency and Simplicity in Self-stabilizing Distributed Depth-first Token Circulation Algorithms

The self-stabilizing distributed depth-rst token circulation algorithms have many applications in distributed systems. The solution to this problem can be used to solve the mutual exclusion, spanning tree construction, synchronization, and many others. In this thesis, we propose several depth-rst token circulation algorithms for trees and arbitrary networks. The algorithms do not use the processor identities, except the root. We used either the state model Dij74] or the message-passing model. In the state model, each processor can read its own state and the states of its neighbors. In this model, a connguration (referred to as statess from now onwards) of the distributed system is expressed as a n-tuple of the processor states, where n is the number of processors in the network. The minimal number of states that each processor is required to have to circulate a token has been extensively studied for the linear chain or ring networks. In his pioneering paper , Dijkstra Dij74] proposed a mutual exclusion algorithm requiring 3 n states for rings. In the same paper, Dijkstra also proposed another mutual exclusion algorithm which needs 2 2 4 (n?2) states for chains. Ghosh Gho93] proposed an alternative solution to Dijkstra's 4-state algorithm on a chain. Tchuente Tch81] showed that with Dijkstra's assumptions, the two algorithms proposed by Dijk-stra are optimal in the number of states. So, it seemed to be impossible to design a deterministic token passing algorithm requiring less states than that used in Dijk-stra's algorithms. However, Flatebo and Datta in FD94] and Ghosh in Gho91] proposed algorithms requiring 2 n states only. But their solutions work only on special networks which are much more restrictive than a simple ring or a chain.