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In the self-stabilizing algorithmic paradigm for distributed computation each node has only a local view of the system, yet in a finite amount of time, the system converges to a global state satisfying some desired property. In this paper we present polynomial time self-stabilizing algorithms for finding a dominating bipartition, a maximal independent set, and a minimal dominating set in any graph.

We propose a new family of interconnection networks that are Cayley graphs with constant node degree 4. These graphs are regular, have logarithmic diameter and are maximally fault tolerant. We investigate different algebraic properties of these networks (including fault tolerance) and propose optimal routing algorithms. As far as we know, this is the first family of Cayley graphs of constant degree 4.

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We propose two distributed algorithms to maintain, respectively, a maximal matching and a maximal independent set in a given ad hoc network; our algorithms are fault tolerant (reliable)

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ÐMulticast communication is a key issue in almost all applications that run on any parallel architecture and, hence, efficient implementation of of multicast is critical to the performance of multiprocessor machines. Multicast is implemented in parallel architectures either via software or via hardware. Software-based approaches for implementing multicast can result in high message latencies, while hardware-based schemes can greatly improve performance. Deadlock freedom in multicast communication is much more difficult to achieve resulting in more involved routing algorithms and higher startup delays. Hardware tree-based algorithms do not require these high startup delays, but do suffer from high probabilities of message blocking leading to poor performance. In this paper, we propose a new hardware tree-based routing algorithm (HTA) for multicast communication under virtual cut-through switching in k-ary n-cubes that outperforms existing software and hardware path-based multicast routing schemes. Simulation results are compared against several commonly used multicast routing algorithms and show that HTA performs extremely well under many different conditions.