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. Author manuscript; available in PMC: 2010 Oct 25.
Published in final edited form as: Ann Math Artif Intell. 2008 Nov 1;54(1-3):3–51. doi: 10.1007/s10472-009-9132-y
Algorithm 4: Elim -Cons PE
input: A belief network = {P1, …, Pn} where Pi's are assume to have a sparse representation; A constraint expression over k variables, = {RQ1, …, RQt} an ordering d = {X1, …, Xn}
output: The belief P().
1 Place buckets with observed variables last in d (to be processed first) // Initialize
Partition and into bucket1, …, bucketn, where bucketi contains all CPTs and constraints whose highest variable is Xi
Let S1, …, Sj be the scopes of the CPTs, and Q1, …Qt be the scopes of the constraints.
We denote probabilistic functions as λ s and constraints by Rs
2 for pn down to 1 do // Backward
 Let λ1, …, λj be the functions and R1, …, Rr be the constraints in bucketp
Process-bucket-RELp(Σ, (λ1, …, λj),(R1, …, Rr))
3 return P() as the result of processing bucket1.