On Finding Optimal Polytrees

Inferring probabilistic networks from data is a notoriously difficult task. Under various goodness-of-fit measures, finding an optimal network NP-hard, even if restricted to polytrees of bounded in-degree. Polynomial-time algorithms are known only for rare special cases, perhaps most notably branchings, that is, in which the in-degree every node at one. Here, we study complexity polytree can be turned into branching by deleting some number arcs or nodes, treated as parameter. We show problem solved via matroid intersection formulation polynomial time deleted constant. The order bound depends on this constant, hence algorithm does not establish fixed-parameter tractability when parameterized arcs. version allows and scales well with contrast positive result showing parameterize somewhat more powerful parameter, tractable, subject complexity-theoretic assumption.