Making a Network Orchard by Adding Leaves

Authors Leo van Iersel , Mark Jones, Esther Julien , Yukihiro Murakami

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Leo van Iersel
  • Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands
Mark Jones
  • Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands
Esther Julien
  • Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands
Yukihiro Murakami
  • Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands

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Leo van Iersel, Mark Jones, Esther Julien, and Yukihiro Murakami. Making a Network Orchard by Adding Leaves. In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Phylogenetic networks are used to represent the evolutionary history of species. Recently, the new class of orchard networks was introduced, which were later shown to be interpretable as trees with additional horizontal arcs. This makes the network class ideal for capturing evolutionary histories that involve horizontal gene transfers. Here, we study the minimum number of additional leaves needed to make a network orchard. We demonstrate that computing this proximity measure for a given network is NP-hard and describe a tight upper bound. We also give an equivalent measure based on vertex labellings to construct a mixed integer linear programming formulation. Our experimental results, which include both real-world and synthetic data, illustrate the efficiency of our implementation.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Trees
  • Mathematics of computing → Graph algorithms
  • Applied computing → Biological networks
  • Applied computing → Bioinformatics
  • Phylogenetics
  • Network
  • Orchard Networks
  • Proximity Measures
  • NP-hardness


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