On the Maximum-entropy Extensions of Probability Measures over Undirected Graphs 1
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چکیده
Two problems: 1. whether a given family of discrete probability measures indexed by the maximal cliques of an undirected graph can be extended, and 2. how to compute explicitly the extension having maximal Shannon entropy, are examined from the point of view of graph decompositions. Close product formula for the extensions is presented and its algo-rithmical complexity is evaluated. Two conjectures on optimality of our decompositions in both problems are put forward.
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