On linear schedules of task graphs for generalized logp-machines

We discuss linear schedules of task-graphs under the communication cost model of the LogP-machine. In addition to our previous work, we consider also non-constant parameters L, o and g, i.e. we introduce messages of different sizes into the LogP-model. The main results of this work are the following: (i) in the LogP-model, less communication in linear schedules does not necessarily imply a better performance. (ii) We give an upper time bound on the execution time of linear clusterings. (iii) We give an efficient algorithm which computes linear clusterings with a minimum number of clusters.