Knowledge compilation structures such as MDDs have been proposed as a way to compile CSPs, to make requests tractable online, in cases where solving is not possible. This paper studies the interest in relaxing two assumptions usually imposed on MDDs, static ordering and read-once property, using a new compilation structure called Set-labeled Diagrams, which are compiled by tracing the search tree explored by a CSP solver. The impact of read-once and static ordering is assessed by simply playing on the variable choice heuristics used during search in the CSP solver.
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