# Alpha Expansion algorithm over graph with vertices having different sets of labels

The alpha-expansion algorithm described here (Probabilistic Graphical Models: Principles and Techniques By Daphne Koller, Nir Friedman, Page 593: algorithm 13.5), is designed for graphs where each vertex has the same set of labels. I am interested in a more general problem where each vertex can have different set of labels having different cardinalities.

Can the alpha-expansion algorithm be used in such cases?

For example, let the graph have 3 vertices. The first vertex can assume labels (a1, a2, a3). The second vertex can assume labels (b1, b2) and the third one can have (c1, c2, c3, c4, c5). The node and edge potentials are defined accordingly. Can alpha-expansion still help me in finding an optimal (approximate) label combination?