We introduce a new type of fully computable problems, for DSS dedicated to maximal spanning tree problems, based on deduction and choice: preferential consistency problems. To show its interest, we describe a new compact representation of preferences specific to spanning trees, identifying an efficient maximal spanning tree sub-problem. Next, we compare this problem with the Pareto-based multiobjective one. And at last, we propose an efficient algorithm solving the associated preferential consistency problem.
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