Linear Programming Formulations for Computing Graph Layout Parameters

Luttamguzi et al. [(2005) Integer Programming Methods for Several Optimization Problems in Graph Theory. Proc. Int. Conf. Computers and Their Applications, CATA 2005, New Orleans, LA, USA, March 16–18, pp. 50–55. ISCA] have introduced a useful framework for the formulation of graph layout parameters measuring number of edges, which is applied to give linear programming formulations for computing the cut-width, minimum linear arrangement and band-width of a graph. We extend the framework of Luttamguzi et al. by the efficient formulation of sets of vertices of the same neighborhood—so-called groups—using binary linear programming (BIP) conditions. We apply our methods in order to find first BIP formulations for computing the important graph layout para-me-ters path-width, neighborhood-width, linear NLC-width, and linear clique-width. Our formulations give useful and new characterizations of the problems as well as easy-to-understand algorithms for their solution. The size of our formulations is polynomial in the size of the input graph.