Abstract
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 \({\mathcal{O}(1.9172^n)}\). 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.
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Gaspers, S., Saurabh, S., Stepanov, A.A. (2008). A Moderately Exponential Time Algorithm for Full Degree Spanning Tree. In: Agrawal, M., Du, D., Duan, Z., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2008. Lecture Notes in Computer Science, vol 4978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79228-4_42
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DOI: https://doi.org/10.1007/978-3-540-79228-4_42
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