A sufficiently fast algorithm for finding close to optimal clique trees

We offer an algorithm that finds a clique tree such that the size of the largest clique is at most (2 alpha + 1)k where k is the size of the largest clique in a clique tree in which this size is minimized and or is the approximation ratio of an alpha -approximation algorithm for the 3-way vertex cut problem. When alpha = 4/3, our algorithm's complexity is O(2(4.67k)n . poly(n)) and it errs by a factor of 3.67 where poly(n) is the running time of linear programming. This algorithm is extended to find clique trees in which the state space of the largest clique is bounded. When k = O(log n), our algorithm yields a polynomial inference algorithm for Bayesian networks. (C) 2001 Elsevier Science B.V. All rights reserved.