  Deciding what to sense is a crucial task, made harder by dependencies and by
a nonadditive utility function. We develop approximation algorithms for
selecting an optimal set of measurements, under a dependency structure modeled
by a tree-shaped Bayesian network (BN). Our approach is a generalization of
composing anytime algorithm represented by conditional performance profiles.
This is done by relaxing the input monotonicity assumption, and extending the
local compilation technique to more general classes of performance profiles
(PPs). We apply the extended scheme to selecting a subset of measurements for
choosing a maximum expectation variable in a binary valued BN, and for
minimizing the worst variance in a Gaussian BN.
