Besides search, complete inference methods can also be used to solve soft constraint
problems. Their main drawback is the high spatial complexity. To improve its practical
usage, we present an approach to decrease memory consumtion in tree decomposition
methods, a class of complete inference algorithms. This approach, called function filtering,
allows to detect and remove some tuples that appear to be consistent (with a cost below the
upper bound) but that will become inconsistent (with a cost exceeding the upper bound) …

… Definition 4 The function filtering operation applied to a function f from a set of functions H,
noted f … A Filtering Tree decomposition … • Filtering is a way of using other functions of
other clusters, parts of functions of other clusters, sums and approximations of functions of
other clusters. …