In this paper, we address the job scheduling problem in a partitionable mesh-connected system when jobs require square meshes and the system is a square mesh of size a power of two. We present a heuristic algorithm of time complexity O(n(log n + log p))where n is the number of jobs to be scheduled and p is the size of the system. The algorithm adopts the Iargesf job jirst scheduling policy and uses a two-dimensional buddy system as the system partitioning scheme. It is shown that in the worst case, the algorithm produces a schedule four times longer than an optimal schedule. On the average, schedules generated by the algorithm are about twice longer than optimal schedules. Index Terms-Approximation algorithm, asymptotic performance bound, job scheduling, NP-hard, partitionable meshconnected system, system partitioning scheme, two-dimensional buddy system.

The known fast sequential algorithms for multiplying two N N matrices (over an arbitrary ring) have time complexity O(N), where 2 < < 3. The current best value of is less than 2.3755. We show that for all 1 p N , m ultiplying two N N matrices can be performed on a p-processor linear array with a recon gurable pipelined bus system (LARPBS) in O N p + N 2 p 2= log p time. This is currently the fastest parallelization of the best known sequential matrix multiplication algorithm on a distributed memory parallel system. In particular, for all 1 p N 2:3755 , m ultiplying two N N matrices can be performed on a p-processor LARPBS in O N 2:3755 p + N 2 p 0:8419 log p time, and linear speedup can be achieved for p as large as O(N 2:3755 =(log N) 6:3262). Furthermore, multiplying two N N matrices can be performed on an LARPBS with O(N) processors in O(log N) time. This compares favorably with the performance on a PRAM.

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We evaluate the average-case performance of three approximation algorithms for online non-clairvoyant scheduling of parallel tasks with precedence constraints. We show that for a class of wide task graphs, when task sizes are uniformly distributed in the range [1..C], the online non-clairvoyant scheduling algorithm LL-SIMPLE has an asymptotic average-case performance bound ofwhere M is the number of processors. For arbitrary probability distributions of task sizes, we present numerical and simulation data to demonstrate the accuracy of our general asymptotic average-case performance bound. We also report extensive experimental results on the average-case performance of online non-clairvoyant scheduling algorithms LL-GREEDY and LS. Algorithm LL-GREEDY has better performance than LL-SIMPLE by using an improved algorithm to schedule independent tasks in the same level. Algorithm LS produces even better schedules due to break of boundaries among levels.