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In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diiusion limited aggregation and several widely used algorithms for equilibrat-ing the Ising model are shown to be highly sequential; it is unlikely they can be… (More)

This paper investigates the parallel complexity of several non-equilibrium growth models. Invasion percolation, Eden growth, ballistic deposition and solid-on-solid growth are all seemingly highly sequential processes that yield self-similar or self-affine random clusters. Nonetheless, we present fast parallel randomized algorithms for generating these… (More)

- Geir Agnarsson, Raymond Greenlaw, Magn Us, M Halldd
- 2000

The k-th power of a graph G is a graph on the same vertex set as G, where a pair of vertices is connected by an edge if they are of distance at most k in G. We study the structure of powers of chordal graphs and the complexity of coloring them. We start by giving new and constructive proofs of the known facts that any power of an interval graph is an… (More)

This paper serves two purposes. Firstly, it is an elementary introduction to the theory of P-completeness | the branch of complexity theory that focuses on identifying the problems in the class P that are \hardest," in the sense that they appear to lack highly parallel solutions. That is, they do not have parallel solutions using time polynomial in the… (More)

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)

- 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)

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)