[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85388-en":3,"doc-seo-85388-105":30,"detail-sidebar-cat-0-en-105":84},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},85388,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Making a Network Orchard by Adding Leaves","Phylogenetic networks model evolutionary histories that include reticulate processes such as hybridization and horizontal gene transfer, which cannot be represented by a single tree. The orchard network class is interpretable as trees augmented with additional horizontal arcs, making it suitable for scenarios where every reticulation corresponds to HGT. The work studies the minimum number of extra leaves required to transform a given network into an orchard. It proves NP-hardness for the proximity computation, provides a tight upper bound, and presents an MILP formulation supported by experiments on real and synthetic data.","arXiv :2305 .03106v2 [math .CO] 8 May 2023  \nMaking a Network Orchard by Adding Leaves Leo van Iersel !   \nDelft Institute of Applied Mathematics, Delft University of Technology, The Netherlands Mark Jones !   \nDelft Institute of Applied Mathematics, Delft University of Technology, The Netherlands Esther Julien !   \nDelft Institute of Applied Mathematics, Delft University of Technology, The Netherlands Yukihiro Murakami 1 !   \nDelft Institute of Applied Mathematics, Delft University of Technology, The Netherlands  \n~~ Abstract ~~  \nPhylogenetic 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 effectiveness of our implementation.  \n2012 ACM Subject Classification Mathematics of computing → Trees; Mathematics of computing → Graph algorithms; Applied computing → Biological networks; Applied computing → Bioinformatics  \nKeywords and phrases Phylogenetics, Network, Orchard Networks, Proximity Measures, NPhardness  \nDigital Object Identifier 10.4230/LIPIcs...  \nSupplementary Material Source Code: [https://github.com/estherjulien/OrchardProximity](https://github.com/estherjulien/OrchardProximity)  \nFunding Leo van Iersel: Research funded in part by Netherlands Organization for Scientific Research (NWO) grants OCENW.KLEIN.125 and OCENW.GROOT.2019.015 .  \nMark Jones: Research funded by Netherlands Organization for Scientific Research (NWO) grant OCENW.KLEIN.125.  \nEsther Julien: Research funded by Netherlands Organization for Scientific Research (NWO) grant OCENW.GROOT.2019.015.  \n 1  Introduction  \nPhylogenetic trees are used to represent the evolutionary history of species. While they are effective for illustrating speciation events through vertical descent, they are insufficientin representing more intricate evolutionary processes. Reticulate (net-like) events such as hybridization and horizontal gene transfer (HGT) can give rise to signals that cannot be represented on a single tree [9, 21] . In light of this, phylogenetic networks have gained increasing attention due to their capability in elucidating reticulate evolutionary processes.  \nPhylogenetic networks are often categorized into different classes based on their topological features. These are often motivated computationally, but some classes are also defined based on their biological relevance [16] . Classical examples of network classes involve the tree-child  \n1 Corresponding author  \n© Leo van Iersel, Mark Jones, Esther Julien, and Yukihiro Murakami; licensed under Creative Commons License CC-BY 4.0  \nLeibniz International Proceedings in Informatics  \nSchloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany  \nXX:2 Making a Network Orchard by Adding Leaves  \nFigure 1 A network on 11 different taxa (excluding unsampled taxon) of fungi including 5 reticulations, which is part of a larger network from [18] . The directed arcs in the figure are linking arcs, which represent gene transfer highways. In order to make all linking arcs horizontal, we require an additional leaf (unsampled taxon) to represent the evolutionary history.  \nnetworks [3] and the tree-based networks [8] . Roughly speaking, tree-child networks are those where every vertex has passed on a gene via vertical descent to an extant species, and tree-based networks are those obtainable from a tree by adding so-called li","cbCaid7G5xMUJMEf","https://ap.wps.com/l/cbCaid7G5xMUJMEf","pdf",1261582,5,1,19,"English","en",105,"# Abstract\n# Introduction\n## Phylogenetic networks and orchard networks\n## Leaf additions and LOR-Distance (Decision)","[{\"question\":\"What is the computational complexity of computing the leaf-addition proximity?\",\"answer\":\"Computing the proximity measure (minimum leaf additions) for a given network is NP-hard, and the paper also provides a tight upper bound.\"}]",1784203071,48,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":79,"head_meta":81,"extra_data":83,"updated_unix":28},"making-a-network-orchard-by-adding-leaves","",{"@graph":36,"@context":78},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/making-a-network-orchard-by-adding-leaves/85388/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72],{"name":73,"@type":74,"acceptedAnswer":75},"What is the computational complexity of computing the leaf-addition proximity?","Question",{"text":76,"@type":77},"Computing the proximity measure (minimum leaf additions) for a given network is NP-hard, and the paper also provides a tight upper bound.","Answer","https://schema.org",{"og:url":52,"og:type":80,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":82,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":85},[86,90,94,98,102,107,112,115,120,123,127],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":87,"show_sort_weight":88,"slug":89},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":91,"show_sort_weight":92,"slug":93},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":22,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":20,"slug":129},"General","general"]