Tractable Disjunctions of Linear Constraints

We study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and inequations with at most one inequality per disjunction. This new class of constraints extends the class of generalized linear constraints originally studied by Lassez and McAloon. We show that deciding consistency of a set of constraints in this class can be done in polynomial time. We also present a variable elimination algorithm which is similar to Fourier's algorithm for linear inequalities. Finally, we use these results to improve the best known temporal reasoning algorithms for the Ord-Horn subclass of Allen's interval formalism. This answers an open question posed by Nebel and B urckert.