Casos especiais ótimos de algoritmos aproximativos para problemas de escalonamento com restrições de precedência em processadores paralelos idênticos

Abstract

This dissertation addresses the class of job scheduling problems with precedence constraints and unit execution times, in identical parallel processors. Such a class of problems is of great importance in computational complexity theory, since small varia- tions in the conditions involved in scheduling make an easy problem very difficult. Two major problems involve the condition of the number of processors, where, if the number of processors is variable, given as input, such problem is proved to be NP-complete, but if the number of processors is fixed, the problem is still open. In this context, the focus of the research involves the problem already proven to be NP-complete, where for which we investigated the main approximation algorithms in the literature and their proofs of approximation ratio of the optimal, such as of the Garey & Jonhson’s 2-approximation algorithm, of the Hu, of the Coffman & Graham, and of the Gangal & Ranade with 2 − (7/(3P + 1)), the best approximation ratio in the literature. The approximation ratio proofs of such algorithms were detailed. As the main contribution of this research, were proved the optimality for specific classes of acyclic directed graphs involving trees (prece- dence trees, such as in-tree and out-tree) for the best approximation algorithms literature.