Unital Dilations of Completely Positive Semigroups

Dilations of completely positive semigroups to endomorphism semigroups have been studied by numerous authors. Most existing dilation theorems involve a non-unital embedding, corresponding to the embedding of $B(H)$ as a corner of $B(K)$ for Hilbert spaces $H \subset K$. A 1986 paper of Jean-Luc Sauvageot shows how to achieve a unital dilation, but does not specify how to do so while also preserving continuity properties of the original semigroup. This thesis further develops Sauvageot's dilation theory in order to establish the existence of continuous unital dilations, and to explore connections with free probability.Comment: 171 pages. Ph. D. thesis; upon graduation, will be published by ProQuest in cooperation with The University of Iow

A Static Scheduling Algorithm Using Dynamic Critical Path For Assigning Parallel Algorithms Onto Multiprocessors

algorithm for compile-time static scheduling of task graphs onto multiprocessors is proposed. The proposed algorithm, which is called Dynamic Critical Path (DCP) scheduling algorithm, is different from previously reported algorithms in a number of ways. First, it determines the critical path of the task graph and selects the next node to be scheduled in a dynamic fashion. Second, it rearranges the schedule on each processor dynamically in the sense that the positions of the nodes in the partial schedules are not fixed until all nodes have been considered. Third, it uses an intelligent way to select a suitable processor for a node by looking ahead the potential start times of the remaining critical nodes on that processor and by scheduling relatively less important nodes to the processors already in use. Four related scheduling algorithms are also discussed. Although these algorithms are efficient in general, they possess drawbacks which can lead to poor performance. The proposed DCP algorithm overcomes the drawbacks of these algorithms and outperforms them by a considerable margin. Despite having a number of new features, the DCP algorithm is fast, efficient in terms of the number of processors used and is equally suitable for different types of graph structures.