10 The question of efficient characterization of inclusion neighbourhood is crucial in some 11 methods for learning (equivalence classes of) Bayesian networks. In this paper, neighbouring 12 equivalence classes of a given equivalence class of Bayesian networks are characterized effi13 ciently in terms of the respective essential graph. One can distinguish two kinds of inclusion 14 neighbours: u...

A general novel approach mapping discrete, combinatorial, graph-theoretic problems onto " physical " models-namely n simplexes in n−1 dimensions-is applied to the graph equivalence problem. It is shown to solve this long standing problem in polynomial, short, time.

We present a polynomial time reduction from the multi-graph isomorphism problem to of code equivalence additive codes over finite extensions ${\mathbb F}_2$.

A graph dynamical system consists of an undirected graph Y where each vertex is assigned a state from a finite set K, an update function for each vertex that depends only on the state of the vertex and its neighbors, and a method that dictates how to compose these functions. A common subclass of graph dynamical systems are sequential dynamical systems, or SDSs, where the update functions are ap...

The property of an allocation rule to be implementable in dominant strategies by a unique payment scheme is called revenue equivalence. We give a characterization of revenue equivalence based on a graph theoretic interpretation of the incentive compatibility constraints. The characterization holds for any (possibly infinite) outcome space and many of the known results are immediate consequences...

We study the process theoretic notion of stuttering equivalence in the setting of parity games. We demonstrate that stuttering equivalent vertices have the same winner in the parity game. This means that solving a parity game can be accelerated by minimising the game graph with respect to stuttering equivalence. While, at the outset, it might not be clear that this strategy should pay off, our ...