General Routing Algorithms for Star Graphs

In designing algorithms for a specific parallel architecture, a programmer has to cope with topological and cardinality variations. Both these problems always increase the programmer\u27s effort. However, an ideal shared memory abstract parallel model called the parallel random access machine (PRAM) [KRUS86, KRUS88] that avoids these problems and also simple-to-program has been proposed. Unfortunately, the PRAM does not seem to be realizable in the present or even foreseeable technologies. On the other hand, a packet routing technique can be employed to simulate the PRAM on a feasible parallel architecture without significant loss of efficiency. The problem of routing is also important due to its intrinsic significance in distributed processing and its important role in the simulations among parallel models. The routing problem is defined as follows: Given a specific network and a set of packets of information in which a packet is an (origin, destination) pair. To start with, the packets are placed on their origins, one per node. These packets must be routed in parallel to their own destinations such that at most one packet passes through any link of the network at any time and all packets arrive at their destinations as quickly as possible. We are interested in a special case of the general routing problem called permutation routing in which the destinations form some permutation of the origins. A routing algorithm is said to be oblivious if the path taken by each packet is only dependent on its source and destination. An oblivious routing strategy is preferable since it will lead to a simple control structure for the individual processing elements. Also oblivious routing algorithms can be used in a distributed environment. In this paper we are concerned with only oblivious routing strategies

Parallel computation on sparse networks of processors

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On the implementation of P-RAM algorithms on feasible SIMD computers

The P-RAM model of computation has proved to be a very useful theoretical model for exploiting and extracting inherent parallelism in problems and thus for designing parallel algorithms. Therefore, it becomes very important to examine whether results obtained for such a model can be translated onto machines considered to be more realistic in the face of current technological constraints. In this thesis, we show how the implementation of many techniques and algorithms designed for the P-RAM can be achieved on the feasible SIMD class of computers. The first investigation concerns classes of problems solvable on the P-RAM model using the recursive techniques of compression, tree contraction and 'divide and conquer'. For such problems, specific methods are emphasised to achieve efficient implementations on some SIMD architectures. Problems such as list ranking, polynomial and expression evaluation are shown to have efficient solutions on the 2—dimensional mesh-connected computer. The balanced binary tree technique is widely employed to solve many problems in the P-RAM model. By proposing an implicit embedding of the binary tree of size n on a (√n x√n) mesh-connected computer (contrary to using the usual H-tree approach which requires a mesh of size ≈ (2√n x 2√n), we show that many of the problems solvable using this technique can be efficiently implementable on this architecture. Two efficient O (√n) algorithms for solving the bracket matching problem are presented. Consequently, the problems of expression evaluation (where the expression is given in an array form), evaluating algebraic expressions with a carrier of constant bounded size and parsing expressions of both bracket and input driven languages are all shown to have efficient solutions on the 2—dimensional mesh-connected computer. Dealing with non-tree structured computations we show that the Eulerian tour problem for a given graph with m edges and maximum vertex degree d can be solved in O(d√n) parallel time on the 2 —dimensional mesh-connected computer. A way to increase the processor utilisation on the 2-dimensional mesh-connected computer is also presented. The method suggested consists of pipelining sets of iteratively solvable problems each of which at each step of its execution uses only a fraction of available PE's