We survey routing problems on fixed-connection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, k-relation routing, routing to random destinations, dynamic routing, isotonic routing, fault tolerant routing, and related sorting results. We also provide a list of unsolved problems and numerous references.

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We present three different specifications of a read-write register that may occasionally return out-of-date values — namely, a (basic) random register, a P-random register, and a monotone random register. We show that these specifications are implemented by the probabilistic quorum algorithm of Malkhi, Reiter, Wool, and Wright, and we illustrate how to program with such registers in the framework of Bertsekas, using the notation of Üresin and Dubois. Consequently, existing iterative algorithms for a significant class of problems (including solving systems of linear equations, finding shortest paths, constraint satisfaction, and transitive closure) will converge with high probability if executed in a system in which the shared data is implemented with registers satisfying the new specifications. Furthermore, the algorithms in this framework will inherit positive attributes concerning load and fault-tolerance from the underlying register implementation. The expected convergence time for iterative algorithms using the monotone implementation is analyzed and shown experimentally to improve on that of the original implementation. The message complexity for iterative algorithms using the monotone probabilistic quorum implementation is shown to improve on that of non-probabilistic implementations in a quantifiable situation.

This paper studies relations between the parallel random access machine (pram) model, and the reconfigurable mesh (rmesh) model, by providing mutual simulations between the models. We present an algorithm simulating one step of an (n lg lg n)- processor crcw pram on an n \Theta n rmesh with delay O(lg lg n) with high probability. We use our pram simulation to obtain the first efficient self-simulation algorithm of an rmesh with general switches: An algorithm running on an n \Theta n rmesh is simulated on a p \Theta p rmesh with delay O((n=p) 2 + lg n lg lg p) with high probability, which is optimal for all p n= p lg n lg lg n. Finally, we consider the simulation of rmesh on the pram. We show that a 2 \Theta n rmesh can be optimally simulated on a crcw pram in \Theta(ff(n)) time, where ff(\Delta) is the slow-growing inverse Ackermann function. In contrast, a pram with polynomial number of processors cannot simulate the 3 \Theta n rmesh in less than \Omega\Gammaha n= lg lg n) e...

Introduction A major research area in the University of Paderborn is Parallel Computing. Next to computer scientists, also researchers in mathematics, electrical and machine engineering, and manufacturing technology employ the computation power of parallel and distributed systems. Further, many institutions of our university focus on research related to this topic: the Paderborn Center for Parallel Computing (PC 2 ) offers support for efficient, comfortable use of parallel machines not only to users of the Paderborn or other universities, but also to users in international industries. Parallel computing in the Heinz Nixdorf Institute and its DFG-Graduate College ranges from basic research to applications in manufacturing technology. The C-LAB, a joint venture with Siemens Nixdorf Informationssysteme AG, contributes design methodology for complex distributed real time systems. All these activities are supported within numerous projects, by, e.g., DFG, BMBF, EU