Abstract

We study here a combinatorial problem that is motivated by a genre of architecture-independent scheduler for parallel computations. Such schedulers are often used, for instance, when computations are being done by a cooperating network of workstations. The results we obtain expose a control-memory tradeoff for such schedulers, when the computation being scheduled has the structure of a complete binary tree. The combinatorial problem takes the following form. Consider, for each integer N =2 n, a family of n algorithms for linearizing the N-leaf complete binary tree in such away that each nonleaf node precedes its children. For each k 2f1 � 2�:::�ng, the kth algorithm in the family employs k FIFO queues to e ect the linearization, in a manner specified later (cf., [1], [5]- [7]). In this paper, we expose a tradeoff between the number of queues used by eachofthen algorithms | which we view as measuring the control complexity of the algorithm | and the memory requirements of the algorithms, as embodied in the required capacity ofthe largest-capacity queue. Specifically, we prove that, for each k 2f1 � 2�:::�ng, the maximum per-queue capacity, call it Q k(N), for a k-queue algorithm that linearizes an N-leaf complete binary tree satisfies e

Citations