[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85589-en":3,"doc-seo-85589-105":30,"detail-sidebar-cat-0-en-105":91},{"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},85589,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Polylogarithmic Approximation for Covering and Connecting Multi-Interface Networks","Studies how to connect multi-interface wireless IoT networks modeled as graphs, where activating multiple interfaces at vertices enables edges when two devices share an active interface. Interface activation incurs heterogeneous costs depending on the interface type and the activating vertex. Two optimization problems are considered: Coverage (all defined links must be realized) and Connectivity (the realized links must span the network). Solutions minimize either maximum node cost or total cost, focusing on max-cost approximation.","arXiv :2605 .06899v2 [ cs .DS] 12 Jul 2026  \nPolylogarithmic Approximation for Covering and Connecting  \nMulti-Interface Networks  \nMichał Szyfelbein∗ Camille Richer†  \nAbstract  \nWe study problems related to connecting multi-interface networks of wireless devices. These problems can be modeled using graphs, where vertices represent the devices and edges represent potential communication links. Each vertex can activate multiple interfaces, anda connection between two vertices is established if they share at least one common active interface. However, activating an interface induces a cost that depends both on the typeof the interface and on the vertex that activates it. We consider two problems arising in multi-interface networks: Coverage and Connectivity. In the Coverage problem, every connection defined in the network must be established, while in the Connectivity problem, it is only required that the established connections form a subgraph spanning the network. The solution should also minimize either the maximum cost incurred by a node or the total cost incurred by all vertices. In this work we are interested in approximating the former of the two cost criterions.  \nWe model both problems using Integer Linear Programming (ILP) and we design approximation algorithms based on a randomized rounding of the solution of the linear programming relaxation. For the Coverage problem, this yields an O (log n)-approximation algorithm, where n is the number of vertices. This result is tight, since the problem generalizes Set Cover. This improves upon the O (b · log n)-approximation algorithm, where b is a certain graph parameter which can be as large as Ω(n) [Algorithmica ’12] . The same relaxation can also be used to get a k-approximation algorithm, where k is the number of different interfaces. This generalizes a similar result for the homogeneous cost case, where the cost of an interface is the same for all vertices. The main result of our work is an O(log2 n)-approximation algorithm for the Connectivity, which is the first non-trivial approximation for this problem. The algorithm is based on a similar LP relaxation with additional cut constraints to ensure connectivity. The rounding procedure resembles the one for the Coverage but requires amore careful analysis to ensure that the connectivity constraints are satisfied.  \n1 Introduction  \nDesigning Internet of Things (IoT) networks often demands establishing connections between large number of devices, which can be achieved by activating communication interfaces at each of them. However, the devices in the network may vary according to the types of interfaces they have at their availability and the amount of resources a given interface consumes. For example some device may be able to utilize Bluetooth and Wi-Fi connections, while the others may provide Zigbee and Z-Wave interfaces. Since IoT devices are typically resource-constrained, it may be desirable to try to establish every relevant connection, while minimizing the amount of resources required to do so.  \nWe model the above problem using a graph. Every device in the network is represented by a vertex with a set of labels encoding its available interfaces. Two devices can communicate if they are connected by an edge, representing that they are within communication range. A  \n∗ Gdańsk University of Technology, [Poland.](Poland. michal.szyfelbein@pg.edu.pl. ORCID:)[ michal.szyfelbein@pg.edu.pl](Poland. michal.szyfelbein@pg.edu.pl. ORCID:)[. ORCID:](Poland. michal.szyfelbein@pg.edu.pl. ORCID:) 0009-0009-9894-9671  \n†Université Paris-Dauphine, PSL Research University, CNRS, UMR 7243, LAMSADE.  \n[camille.richer@dauphine.eu](camille.richer@dauphine.eu. ORCID:)[. ORCID:](camille.richer@dauphine.eu. ORCID:) 0009-0000-3636-6571  \n(a) Input graph (b) Coverage assignment (c) Connectivity assignment  \nFigure 1: From left to right: a common input graph, a covering assignment, and a connecting assignment for the same instance. An edge is c","cbCaiqURkavRRmGi","https://ap.wps.com/l/cbCaiqURkavRRmGi","pdf",602890,2,1,13,"English","en",105,"# Abstract\n# Introduction\n## Modeling multi-interface network problems\n## Related work","[{\"question\":\"How are multi-interface networks modeled in this work?\",\"answer\":\"Devices are represented as vertices in a graph, and potential communication links are represented as edges. An edge becomes active when the two adjacent vertices share at least one common active interface.\"},{\"question\":\"What is the difference between the Coverage and Connectivity problems?\",\"answer\":\"Coverage requires establishing every defined connection, meaning both endpoints of every edge must share an active interface. Connectivity requires that the established connections form a subgraph spanning all vertices, ensuring overall network connectivity (not necessarily direct edge-by-edge realization).\"},{\"question\":\"What approximation results does the paper present?\",\"answer\":\"For Coverage, the paper obtains an O(log n)-approximation via randomized rounding of an LP relaxation, improving earlier bounds. For Connectivity, it presents an O(log^2 n)-approximation using a similar LP relaxation augmented with cut constraints.\"}]",1784204771,33,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":28},"polylogarithmic-approximation-for-covering-and-connecting-multi-interface-networks","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/polylogarithmic-approximation-for-covering-and-connecting-multi-interface-networks/85589/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"How are multi-interface networks modeled in this work?","Question",{"text":75,"@type":76},"Devices are represented as vertices in a graph, and potential communication links are represented as edges. An edge becomes active when the two adjacent vertices share at least one common active interface.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the difference between the Coverage and Connectivity problems?",{"text":80,"@type":76},"Coverage requires establishing every defined connection, meaning both endpoints of every edge must share an active interface. Connectivity requires that the established connections form a subgraph spanning all vertices, ensuring overall network connectivity (not necessarily direct edge-by-edge realization).",{"name":82,"@type":73,"acceptedAnswer":83},"What approximation results does the paper present?",{"text":84,"@type":76},"For Coverage, the paper obtains an O(log n)-approximation via randomized rounding of an LP relaxation, improving earlier bounds. For Connectivity, it presents an O(log^2 n)-approximation using a similar LP relaxation augmented with cut constraints.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]