Description: 1 Introduction.- 1.1 Parallel computing and communication.- 1.2 Scope of this work.- 1.3 Organization.- 1.4 Model of computation.- 1.5 Graph-theoretic definitions.- 1.6 Basic terminology.- 2 Diamond Dags.- 2.1 Communication requirements of a DAG.- 2.2 The diamond dag.- 2.3 Diamond dags with higher degree vertices.- 2.4 Effects of the tradeoff on performance.- 2.5 Concluding remarks.- 3 Rectangular Dags.- 3.1 The rectangular dag.- 3.2 Lower bound on computation time.- 3.3 Lower bound on data traffic.- 3.4 Lower bound on t * ?.- 3.5 The tradeoff factor for the rectangular dag.- 3.6 Performance considerations.- 3.7 Concluding remarks.- 4 Three and Higher Dimensional Dags.- 4.1 An n X n X n dag.- 4.2 A d-dimensional dag.- 4.3 The effects of tradeoff on performance.- 4.4 Concluding remarks.- 5 Factoring Dense and Sparse Matrices.- 5.1 Dense symmetric positive definite systems.- 5.2 Sparse, symmetric positive definite systems.- 5.3 Concluding remarks.- 6 Conclusions and Some Open Issues.- 6.1 Summary of principal results.- 6.2 Suggestions for further research.

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