  The intelligent reformulation or restructuring of a belief network can
greatly increase the efficiency of inference. However, time expended for
reformulation is not available for performing inference. Thus, under time
pressure, there is a tradeoff between the time dedicated to reformulating the
network and the time applied to the implementation of a solution. We
investigate this partition of resources into time applied to reformulation and
time used for inference. We shall describe first general principles for
computing the ideal partition of resources under uncertainty. These principles
have applicability to a wide variety of problems that can be divided into
interdependent phases of problem solving. After, we shall present results of
our empirical study of the problem of determining the ideal amount of time to
devote to searching for clusters in belief networks. In this work, we acquired
and made use of probability distributions that characterize (1) the performance
of alternative heuristic search methods for reformulating a network instance
into a set of cliques, and (2) the time for executing inference procedures on
various belief networks. Given a preference model describing the value of a
solution as a function of the delay required for its computation, the system
selects an ideal time to devote to reformulation.
