Rank Regression by Projection Method vs Graph-Theoretical Algorithms

In a recent paper in Bobrowski, L. (2007), a method for finding an optimal order of scheduling certain tasks was proposed. Each of the problems is characterized by a vector of features. The proposed method constructs a projection to the time axis which minimizes a certain error functional, using SVM like techniques as studied e.g. in Topczwska, M et al, (2007) and cited there papers. In the considered application, those vectors contained information about the dependence of the considered problem on the other tasks to be scheduled. Zero entries indicate independence, ones mean that the given task needs to wait until the other task is finished, Bobrowski, L. (2007). In this paper, we study medium size examples and compare the performance of the proposed method to an alternative which uses a graph-theoretical approach.