A Comparative Performance Evaluation of Randomized Tree Embedding in Hypercubic Networks

{ An important problem in parallel computing is to embed a task interaction graph into a static network. Dynamic embedding is performed at run-time, where the task interaction graph is not known in advance. In this paper, we investigate the performance of randomized embedding of tree-structured parallel computations (i.e., where the task interaction graph is a tree) into the classic hypercubic networks. Our method is to use recurrence relations and linear systems of equations that characterize the expected load on each processor. We demonstrate numerical data, and make a number of interesting observations.