Journal of Graph Algorithms and Applications
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The SNPR neighbourhood of tree-child networks
Vol. 22, no. 2, pp. 329-355, 2018. Regular paper.
Abstract Network rearrangement operations like SNPR (SubNet Prune and Regraft), a recent generalisation of rSPR (rooted Subtree Prune and Regraft), induce a metric on phylogenetic networks. To search the space of these networks one important property of these metrics is the sizes of the neighbourhoods, that is, the number of networks reachable by exactly one operation from a given network. In this paper, we present exact expressions for the SNPR neighbourhood of tree-child networks, which depend on both the size and the topology of a network. We furthermore give upper and lower bounds for the minimum and maximum size of such a neighbourhood.
Submitted: July 2017.
Reviewed: January 2018.
Revised: January 2018.
Reviewed: April 2018.
Revised: April 2018.
Accepted: July 2018.
Final: July 2018.
Published: August 2018.
Communicated by Fabio Vandin