On Computing the Minimal Labels in Time Point Algebra Networks

We analyze the problem of computing the minimal labels for a network of temporal relations in the Point Algebra. van Beek proposes an algorithm for accomplishing this task which takes O(max(n 3 ; n 2 \Delta m)) time (for n points and m 6=-relations). We show that the proof of the correctness of this algorithm given by van Beek and Cohen is faulty, and we provide a new proof showing that the algorithm is indeed correct. Keywords: temporal reasoning, Point Algebra, constraint networks, reasoning with inequations The work of the first author was carried out in part during a visit at the Computer Science Department of the University of Rochester (NY) supported by the Italian National Research Council (CNR), and in part at IRST in the context of the MAIA project and CNR projects "Sistemi Informatici e Calcolo Parallelo" and "Pianificazione Automatica". The second author was supported by Rome Lab Contract F30602-91-C-0010. 1 Introduction The Interval Algebra (IA) (Allen 1983) and t..

On Computing the Minimal Labels in Time Point Algebra Networks

We analyze the problem of computing the minimal labels for a network of temporal relations in the Point Algebra. van Beek proposes an algorithm for accomplishing this task which takes $O(max(n^3,n^2\cdot m))$ time (for $n$ points and $m$ $\neq$-relations). We show that the proof of the correctness of this algorithm given by van Beek and Cohen is faulty, and we provide a new proof showing that the algorithm is indeed correct