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.

A fundamental challenge for parallel computing is to obtain high-level, architecture independent, algorithms which efficiently execute on general-purpose parallel machines. With the emergence of message passing standards such as MPI, it has become easier to design efficient and portable parallel algorithms by making use of these communication primitives. While existing primitives allow an assortment of collective communication routines, they do not handle an important communication event when most or all processors have non-uniformly sized personalized messages to exchange with each other. We focus in this paper on the h-relation personalized communication whose efficient implementation will allow high performance implementations of a large class of algorithms. While most previous h-relation algorithms use randomization, this paper presents a new deterministic approach for h-relation personalized communication with asymptoticaly optimal complexity for h p². As an application, we ...

We consider the problem of routing packets on an n \Theta \Delta \Delta \Delta \Theta n MIMD mesh-connected array of processors augmented with row and column buses. We give lower bounds and randomized algorithms for the problem of routing k-permutations (where each processor is the source and destination of exactly k packets) on a d-dimensional mesh with buses, which we call the (k; d)-routing problem. We give a general class of "hard" permutations which we use to prove lower bounds for the (k; d)-routing problem, for all k; d 1. For the (1; 1)- and (1; 2)-routing problems the worst-case permutations from this class are identical to ones published by other authors, as are the resulting lower bounds. However, we further show that the (1; d) routing problem requires 0:72 \Delta n steps for d = 3, 0:76 \Delta n steps for d = 4 and slightly more than (1 \Gamma 1=d) \Delta n steps for all d 5. We also obtain new lower bounds for the (k; d)-routing problem for k; d ? 1, which improve on t...

This paper provides an overview of lower and upper bounds for algorithms for mesh-connected processor networks. Most of our attention goes to routing and sorting problems, but other problems are mentioned as well. Results from 1977 to 1995 are covered. We provide numerous results, references and open problems. The text is completed with an index. This is a worked-out version of the author's contribution to a joint paper with Miltos D. Grammatikakis, D. Frank Hsu and Miro Kraetzl on multicomputer routing, submitted to the Journal of Parallel and Distributed Computing.

The ASC (MSIMD) model for parallel computation supports a generalized version of an associative style of computing that has been used since the introduction of associative SIMD computers in the early 1970's. In particular, this model supports data parallelism, constant time maximum and minimum operations, one or more instruction streams (ISs) which are sent to an equal number of partition sets of processors, assignment of tasks to the ISs using control parallelism. ASC also allows a network to interconnect the processing elements (PEs). This paper shows how ASC can be simulated with synchronous PRAM, and the converse. These results provide an important step in de ning the power of associative model in terms of PRAM which is the most well studied parallel model. Also, these simulations will provide numerous algorithms for ASC by providing an automatic method ofconverting algorithms from PRAM to ASC.

Routing problems are studied for the Parallel Alternating-Direction Access Machine. The goal is to investigate what level of optimality can be achieved depending on loads of packets per memory unit. In the case of typical moderate loads, our algorithms are optimal to within a small multiplicative constant; a deterministic and a randomized algorithm are developed, both faster than the best previously known routing algorithm. Moreover, for sufficiently large loads, an algorithm which misses optimality by only an additive lower-order term is designed. We consider also off-line routing problems, and multidimensional extension of the model. 1 Introduction The Parallel Alternating-Direction Access Machine, PADAM, is a multiprocessor computer with memory units, MUs, arranged in a grid structure, together with the processing units, PUs. The two-dimensional n \Theta n PADAM has n PUs and n 2 MUs arranged according to the pattern in Figure 1 (notice that there are only n PUs: the PUs marked...

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This paper studies the problems of permutation routing on different mesh models of parallel computation and simulates algorithms for different mesh models using C. Simple algorithms for permutation routing mesh models with and without bus have been considered, analyzed and simulated. In mesh models with bus, models with fixed bus and reconfigurable buses are dealt. For problems in permutation routing on meshes with bus, a technique has been considered that can be used to develop deterministic algorithms that are better than the simpler algorithms. This paper also analyzes one deterministic algorithm derived using the technique for permutation routing on two dimensional networks and implements this algorithm using C. For permutation routing with reconfigurable bus the computational aspects of reconfigurable mesh model has been analyzed and simulating the problem in a simulator called RMSIM. A hardware for the reconfiguration switch is also suggested and implemented in VHDL. The design of the switch is based on restricted configuration model that involves ten different possible configurations. VHDL test pattern analysis for the switch, simulation results for the above-mentioned models are also provided.

The architecture of 'mesh of buses' is an important model in parallel computing. Its main advantage is that the additional broadcast capability can be used to overcome the main disadvantage of the mesh, namely its relatively large diameter. We show that the addition of buses indeed accelerates routing times. Furthermore, unlike in the `store and forward' model, the routing time becomes proportional to the network load, resulting in decreasing in routing time for a smaller number of packets. We consider 1-1 routing of m packets in a d-dimensional mesh with n d processors and d \Delta n d\Gamma1 buses (one per row and column). The two standard models of accessing the buses are considered and compared: CREW, in which only one processor may transmit at any given time on a given bus, and the CRCW model in which several processors may attempt to transmit at the same time (getting a noise signal as a result). We design a routing algorithm that routes m packets in the CREW model ...

Typeset in Palatino by TEX and LATEX 2ε.Except where otherwise indicated, this thesis is my own original work and has not been submitted for any other degree.