We consider the scheduling problem of minimizing the average weighted job completion time on a single machine under precedence constraints. We show that this problem with arbitrary job weights, the special case of the problem where all job weights are one, and several other special cases of the problem all have the same approximability threshold with respect to polynomial time approximation alg...

We examine computational complexity implications for scheduling problems with job precedence relations with respect to strong precedence versus weak precedence. We propose a consistent definition of strong precedence for chains, trees, and series parallel graphs. Using modular decomposition for partially ordered sets (posets), we restate and extend past complexity results for chains and trees a...

We consider the on-line problem of scheduling jobs with precedence constraints on m machines. We concentrate in two models, the model of uniformly related machines and the model of restricted assignment. For the related machines model, we show a lower bound of (p m) for the competitive ratio of deterministic and randomized on-line algorithms, with or without preemptions even for known running t...

We consider the single machine scheduling problem to minimize the average weighted completion time under precedence constrains. Improving on the various 2-approximation algorithms is considered one of the ten most prominent open problems in scheduling theory. Recently, research has focused on special cases of the problem, mostly by restricting the set of precedence constraints to special classe...

The paper introduces value precedence on integer and set sequences. A useful application of the notion is in breaking symmetries of indistinguishable values, an important class of symmetries in practice. Although value precedence can be expressed straightforwardly using if-then constraints in existing constraint programming systems, the resulting formulation is inefficient both in terms of size...

This paper considers the polyhedral structure of the precedence-constrained knapsack problem, which is a knapsack problem with precedence constraints imposed on the set of variables. The problem itself appears in many applications. Moreover, since the precedence constraints appear in many important integer programming problems, the polyhedral results can be used to develop cutting-plane algorit...