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An edge ranking of a graph is a labeling of the edges using positive integers such that all paths between two edges with the same label contain an intermediate edge with a higher label. An edge ranking is optimal if the highest label used is as small as possible. The edge-ranking problem has applications in scheduling the manufacture of complex multi-part… (More)

This paper is concerned with the subclass of graphs called cubic graphs. We survey these graphs and their history. Several classical graph theory results concerning cubic graphs are explained. Graph theory problems whose solutions on cubic graphs are particularly important or interesting are presented both from the sequential and parallel point of view. A… (More)

2 Abstract A model is proposed that can be used to classify algorithms as inherently sequential. The model captures the internal computations of algorithms. Previous work in complexity theory has focused on the solutions algorithms compute. Direct comparison of algorithms within the framework of the model is possible. The model is useful for identifying… (More)

- David Notkin, Lawrence Snyder, David Socha, Mary L. Bailey, Bruce Forstall, Kevin Gates +7 others
- PPOPP/PPEALS
- 1988

Experience from over five years of building nonshared memory parallel programs using the Poker Parallel Programming Environment has positioned us to evaluate our approach to defining and developing parallel programs. This paper presents the more significant results of our evaluation of Poker. The evaluation is driving our next effort in parallel programming… (More)

The paper's main contributions are a compendium of problems that are complete for symmetric logarithmic space (SL), a collection of material relating to SL, a list of open problems, and an extension to the number of problems known to be SL-complete. Complete problems are one method of studying SL, a class for which programming is non-intuitive. Our… (More)

The potential speedup for SIMD parallel implementations of APL programs is considered. Both analytical and (simulated) empirical studies are presented. The approach is to recognize that nearly 95% of the operators appearing in APL programs are either scalar primitive, reduction or indexing and so the performance of these operators gives a good estimate of… (More)