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A new method is presented for job assignment to and reassignment between machines in a computing cluster. Our method is based on a theoretical framework that has been experimentally tested and shown to be useful in practice. This "opportunity cost" method converts the usage of several heterogeneous resources in a machine to a single homogeneous "cost". Assignment and reassignment is then performed based on that cost. This is in contrast to previous methods for job assignment and reassignment, which treat each resource as an independent entity with its own constraints. These previous methods were intrinsically ad hoc, as there was no clean way to balance one resource against another.

Abstract-Heterogeneous systems provide new opportunities to increase the performance of parallel applications on clusters with CPU and GPU architectures. Currently, applications that utilize GPU devices run their device-executable code on local devices in their respective hosting-nodes. This paper presents a package for running OpenMP, C++ and unmodified OpenCL applications on clusters with many GPU devices. This Many GPUs Package (MGP) includes an implementation of the OpenCL specifications and extensions of the OpenMP API that allow applications on one hosting-node to transparently utilize cluster-wide devices (CPUs and/or GPUs). MGP provides means for reducing the complexity of programming and running parallel applications on clusters, including scheduling based on task dependencies and buffer management. The paper presents MGP and the performance of its internals.

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Abstract. Let si" denote a random acyclic directed graph which is obtained from a random graph with vertex set {l, 2, ---, nl, such that each edge is present with a prescribed probability p and all the edges are directed from higher to lower indexed vertices . Define a subset of vertices in si" to be strongly independent if there is no directed path between any pair of vertices in the subset . We show that the sequence J(si" ), the number of vertices in the largest strongly independent vertex subset of si" satisfies with probability tending to 1, 9(4") 1 2 as n ~ oo, .%log n~.%log 1/q where q=1-p.