Total Algorithms

We deene the notion of total algorithms for networks of processes. A total algorithm enforces that a \decision" is taken by a subset of the processes, and that participation of all processes is required to reach this decision. Total algorithms are an important building block in the design of distributed algorithms. For some important network control problems it can be shown that an algorithm solving it is necessarily total, and that any total algorithm can solve the problem. We study some total algorithms for a variety of network topologies. Constructions are shown to derive algorithms for Mutual Exclusion, Election, and Distributed Innmum Approximation from arbitrary total algorithms. The paper puts many results and paradigms about designing distributed algorithms in a general framework. This report outlines several other works of the author. Total algorithms, their properties, and some additional examples, as well as traversal algorithms and the time complexity of distributed algorithms are studied in Tel94, Chap. 6]. The construction of algorithms for distributed innmum approximation is treated in CBT94, Tel86] and Tel91, Sec. 4.1].