Edge-Disjoint Spanning Trees on the Star Network with Applications to Fault Tolerance

Data communication and fault tolerance are important issues in multiprocessor systems. One way to achieve fault tolerant communication is by exploiting and e ectively utilizing the disjoint paths that exist between pairs of source, destination nodes. In this paper we construct a structure, called the multiple edgedisjoint spanning trees, on the star network, denoted by Sn. This is used for the derivation of an optimal single node broadcasting algorithm, which o ers a speed up of n 1 compared to the straightforward single node broadcasting algorithm that uses a single breadth rst spanning tree. It is also used for the derivation of fault tolerant communication algorithms. As a result, fault tolerant algorithms are presented for four basic communication problems: the problem of a single node sending the same message to all other nodes or single node broadcasting, the problem of simultaneous single node broadcasting from all nodes or multinode broadcasting, the problem of a single node sending distinct messages to each one of the other nodes or single node scattering and nally the problem of simultaneous single node scattering from all nodes or total exchange. Fault tolerance is achieved by sending multiple copies of the message through a number of disjoint paths. These algorithms operate successfully in the presence of up to n 1 faulty nodes or edges in the system. They also o er the exibility of controlling the degree of fault tolerance, depending on how reliable the network is. As pointed out in [28], the importance of these algorithms lies in the fact that no knowledge of the faulty nodes or edges is required in advance. All of the algorithms presented make the assumption that each node can exchange messages of xed length with all of its neighbors simultaneously at each time step, i.e. the all-port communication assumption, and that communication is bidirectional.