We consider the problem of learning Bayesian network structures from complete data. In particular, we consider the enumeration of their k-best equivalence classes. We propose a new search space for A* search, called the EC graph, that facilitates the enumeration of equivalence classes, by representing the space of completed, partially directed acyclic graphs. We also propose a canonization of t...

The individualization-refinement paradigm for computing a canonical labeling and/or the automorphism group of a graph is investigated. New techniques are introduced with the aim of reducing the size of the associated search space. In particular, a new partition refinement algorithm is proposed, together with graph invariants having a global nature. Experimental results and comparisons with exis...

In [4], an efficient algorithm for inverting the L-invariant is presented, which amounts to a reduction to resolving a certain combinatorial-design problem, the so-called magic square. While elegant, this approach does not lend itself to generalization to greater numbers of variables. In this paper, I approach the L-canonization problem by explicitly seeking to exploit the well-behaved geometry...

The "Capella Stenoniana" (Niels Stensen chapel) situated in the Basilica of San Lorenzo in Florence is the tomb of the anatomist and founder of modern geology Niels Stensen (1638-1686). It displays commemorative plaques and contains a sarcophagus with Stensen's mortal remains. The tomb of Blessed Stensen, whose canonization process is under way, is always covered with papers with requests for i...

THEOREM A. For every positive integer m there exists a positive integer n such that for every coloring A: (O,..., n 1) + w there exists an arithmetic progression a, a + d,..., a + (m 1)d of length m such that the restriction of A to {a, a + d,..., a + (m l)d} is either a constant or a one-to-one mapping. This theorem is the so called canonical version of van der Waerden’s theorem on arithmetic ...