Complexity studies of a temporal constraint propagation algorithm: a statistical analysis

Abstract

In this paper we have studied the empirical relation between the hardness of the temporal 3-consistency problem with respect to its inherent problem structure. This is a sub-problem of the temporal constraint satisfaction problem (TCSP). The problem structure has been identified with some quantifiable parameters of the constraint graph. Our work is in line with the recent experimental studies of NPcomplete problems, except that in our case a richer repertoire of independent variables make a straight forward study impossible. Hence we have resorted to a deeper statistical analysis in order to develop a regression model as the sought after quantitative empirical relationship between the problem structure and the timecomplexity. Our model shows robustness against repeated experimentation and, a strong predictive power on independent verification. We also hope that this paper will contribute towards the development of a more rigorous experimental methodology in artificial intelligence than what is being practiced now.