A Study on Distributed Structures

2 Preface In distributed and parallel computing environments, there are many computational problems that require efficient communication and coordination between the processes. For such problems there have been proposed several distributed structures, each designed to solve a particular problem or a class of problems. The distributed structures take into account the particularities of the specific problems and provide efficient solutions for them. In this work we study two distributed structures: counting networks and the mesh network. Counting networks are used for implementing distributed counters; mesh is a communication network. So far, counting networks have been used for increment operations only. We demonstrate that counting networks can be extended to support decrement operations as well. Furthermore, we present new efficient counting network constructions. For the mesh network we study the communication problem, known as hot-potato routing, and we provide novel algorithms for the class of hot-potato algorithms known as " greedy. " Although counting networks and the hot-potato routing in the mesh are used for different purposes, their underlying distributed structures share a common characteristic: the basic structural elements contain a very limited amount of memory. Specifically, in counting networks each structural element contains either a single bit of information or a small number of bits; in the mesh, with greedy hot-potato routing, each node doesn't have any amount of memory for storing communication packets in transit. The present thesis is structured as follows. The first chapters are devoted to counting networks; while the last ones to hot-potato routing in the mesh. In particular, in Chapters 1,2, 3, and 4 we study counting networks, and in Chapters 5, 6 and 7 we study hot-potato routing in the mesh. We give our conclusions in Chapter 8.