A Moderately Exponential Time Algorithm for Full Degree Spanning Tree

We consider the well studied Full Degree Spanning Tree problem, a NP-complete variant of the Spanning Tree problem, in the realm of moderately exponential time exact algorithms. In this problem, given a graph G, the objective is to find a spanning tree T of G which maximizes the number of vertices that have the same degree in T as in G. This problem is motivated by its application in fluid networks and is basically a graph-theoretic abstraction of the problem of placing flow meters in fluid networks. We give an exact algorithm for Full Degree Spanning Tree running in time O(1.9172). This adds Full Degree Spanning Tree to a very small list of “non-local problems”, like Feedback Vertex Set and Connected Dominating Set, for which non-trivial (non brute force enumeration) exact algorithms are known.