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 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.