Using Answer Set Programming to Find Maximum Height Spanning Trees

The max tree-height of an undirected graph is the longest possible length of a path among all spanning trees of the graph. A maximum height spanning tree of an undirected graph is a spanning tree that has a path of length equal to the max tree-height of the graph. Finding the max tree-height of a graph, or similarly some spanning tree of maximum height, is an NP-hard optimization problem for which efficient optimal procedures have been proposed only for special classes of graphs, and which is not polynomially approximable within any constant factor unless PTIME = NP. The paper presents an elegant yet efficient and succinct logic program in Answer Set Programming for the identification of both the max tree-height and the maximum height spanning trees of a graph.