  This a nice paper and I think you manage to keep your article easily readable. Specially the figures, such as figure 3, helped me follow your explanations. I haven't finished reading the paper but I have minor remarks/typo: - Page 9 in the definition of multigraph, should e(v, V) be transformed to e({v},V) in order to be completely rigorous? - I don't know what “maximum-entropy sampling” is but why quoting it ? - I don't get the use of Reversible Decompression, apart from being an extreme case of external information. I don't think this case deserve to be explained in detailed, as it does not have any impact on the understanding of the paper. - I find the notation for definition 10 a bit confusing. A Cartesian MultiEdge Partition is made of Cartesian products of two vertex subsets. The notation for each cartesian product uses subscript on vertex subset: $(V_i \times V'_i)$ for the $i$th product. This lead me to think that $(V_i \times V'_i)$ was a possible Cartesian product. This also lead me to think that Cartesian MultiEdge Partition are made of Cartesian product of vertex partition: $B(V \times V) = \{(V_i \times V_j)\}\ \forall V_i \in P_1, V_j \in P_2 \wedge P_1 \in B(V), P_2 \in B(V)$. I think all Cartesian product of vertex partition are Cartesian MultiEdge partition. Is there any Cartesian MultiEdge Partition that is not a Cartesian product of vertex partition? - In the conplete case after definition 11, I don't know the notation $\omega$ for the number of feasible partitions. - I think you missed a $\lambda$ in the lagrange function page 21. Should it be $q_{\lambda}(VVT)= |VVT| + \lambda Loss(VVT)$