Comments on "Design and performance evaluation of load distribution strategies for multiple loads on heterogeneous linear daisy chain networks"

Min, Veeravalli, and Barlas have proposed strategies to minimize the overall execution time of one or several divisible loads on a heterogeneous linear network, using one or more installments [Han Min Wong, Bharadwaj Veeravalli, Scheduling divisible loads on heterogeneous linear daisy chain networks with arbitrary processor release times, IEEE Trans. Parallel Distrib. Syst. 15 (3) (2004) 273-288; Han Min Wong, Bharadwaj Veeravalli, Gerassimos Barlas, Design and performance evaluation of load distribution strategies for multiple divisible loads on heterogeneous linear daisy chain networks, J. Parallel Distrib. Comput. 65 (12) (2005) 1558-1577]. We show using a very simple example that their approach does not always produce a solution and that, when it does, the solution is often suboptimal. We also show how to find an optimal scheduling for any instance, once the number of installments per load is given. Finally, we formally prove that under a linear cost model, as in both the above-mentioned references, an optimal schedule has an infinite number of installments. Therefore such a cost model should not be used to design practical multi-installment algorithms.