[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83795-en":3,"doc-seo-83795-105":29,"detail-sidebar-cat-0-en-105":95},{"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":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},83795,5909877438554,"Maeve","https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272",8,"Research & Report","Mechanism Design for Locating a Bridge Between Regions with Prelocated Facilities","This paper studies a mechanism design problem for locating a bridge between two separate regions, each already equipped with a facility. Agents located in either region privately hold their own locations. After the bridge is built, agents travel to the nearest prelocated facility across the bridge, and individual cost equals the distance to that facility. The work analyzes social cost and maximum cost under strategyproof (SP) mechanisms, strengthening to group-strategyproof (GSP) and strong group-strategyproof (SGSP) variants.","Mechanism Design for Locating a Bridge Between Regions with Prelocated  \nFacilities  \nGenjie Qin 1 , Chenhao Wang2 , Jianan Lin3 , Qizhi Fang 1 , Wenjing Liu 1 ,∗  \n1 School of Mathematical Sciences, Ocean University of China  \n2Beijing Normal University  \n3Rensselaer Polytechnic Institute  \n[qgj@ouc.edu.cn](qgj@ouc.edu.cn), [chenhwang@bnu.edu.cn](chenhwang@bnu.edu.cn), [hcm6755@gmail.com](hcm6755@gmail.com), [qfang@ouc.edu.cn](qfang@ouc.edu.cn), [liuwj@ouc.edu.cn](liuwj@ouc.edu.cn)  \narXiv :2607 .04309v 1 [ cs .GT] 5 Jul 2026  \nAbstract  \nIn many urban planning projects, social planners require the construction of a bridge to connect two regions separated by obstacles such as rivers or highways. This paper studies the mechanism design problem for locating a bridge between two separate regions, each of which has been equipped with a facility. There are a set of agents located in each region and each agent has her location as private information. Once the bridge is built, the agents will go to the nearest facility to receive service and each agent’s cost is the distance from her location to the nearest prelocated facility via the bridge. We investigate social cost and maximum cost under strategyproof (SP) mechanisms, with stronger notions of group-strategyproof (GSP) and strong group-strategyproof (SGSP) .  \nFor the maximum cost objective, we characterize the optimal solution and show that it satisfies GSP. Under the SGSP, we propose a deterministic 3-approximation mechanism and a randomized 2-approximation mechanism, while proving a lower bound of 2 for any deterministic SGSP mechanism.  \nFor the social cost objective, we present a deterministic 3-approximation mechanism and a randomized 2-approximation mechanism that satisfy GSP.  \nWe establish lower bounds of 2 and 1 . 1 for deterministic and randomized SP mechanisms, respectively. Under the SGSP, the lower bound for deterministic mechanisms increases to 1 + min{m, n}, and we provide a (1+2min{m, n})-approximation mechanism. For randomized mechanisms, the lower bound remains 1.1, while an upper bound of (1 + 2mn · (m + n)−1) is achieved.  \n1 Introduction  \nThe facility location problem is an important problem in the field of optimization. Its main goal is to select the best locations to place facilities under given constraints to optimize certain objectives. In the facility location problem, each agent possesses private information that cannot be directly verified by the social planner. This informational asymmetry creates  \nstrategic incentives for agents to misreport their private information to influence the facility placement decision.  \nIn 2013,[Procaccia and Tennenholtz, 2013] employed this problem to introduce their highly influential framework of approximate mechanism design without money. In its standard formulation, the facility location problem tasks a social planner with locating one or two facilities on a real line to minimize either the maximum individual cost or the total social cost, based on the locations reported by agents. Since agents may strategically misreport their positions, the goal is to design mechanisms that are approximately optimal while ensuring truthfulness. The problem has since become a central topic of investigation in theoretical computer science and artificial intelligence.  \nMost existing research focuses on locating facilities in unconnected spaces. While such models provide a foundational theoretical framework, they are often inadequate for addressing a prevalent class of real-world scenarios: two regions, separated by natural or artificial barriers, each already equipped with public service facilities, where a planner aims to construct a bridge to connect them. This enables agents to flexibly access the nearest facility—in either region—based on their real-time locations, thereby reducing travel distance, lowering time costs, and promoting equitable utilization of public resources.  \nThe essence of this “bridge location problem” is fu","cbCaiisSziF60JGJ","https://ap.wps.com/l/cbCaiisSziF60JGJ","pdf",1392894,1,12,"English","en",105,"# Introduction\n## Problem background: facility location and strategic reporting\n## Bridge location setting and modeling assumptions\n## Prior work and research gap\n## Paper contributions and mechanism results","[{\"question\":\"What are agents optimizing after the bridge is built, and how is their cost defined?\",\"answer\":\"After the bridge is constructed, each agent goes to the nearest prelocated facility in either region. An agent’s cost is the distance from her private location to that nearest facility via the bridge.\"},{\"question\":\"Which objectives does the paper analyze under strategyproof-type mechanisms?\",\"answer\":\"It examines both maximum individual cost and total social cost objectives under SP mechanisms, and also under stronger group-strategyproof (GSP) and strong group-strategyproof (SGSP) notions.\"},{\"question\":\"What approximation results are provided under the maximum-cost objective?\",\"answer\":\"For maximum cost, the paper characterizes the optimal solution satisfying GSP, proposes deterministic 3-approximation and randomized 2-approximation mechanisms under SGSP, and proves a deterministic SGSP lower bound of 2.\"},{\"question\":\"How do the lower bounds differ between deterministic and randomized mechanisms for the social-cost objective?\",\"answer\":\"For deterministic SP mechanisms, the paper gives a lower bound of 2, while for randomized SP mechanisms it gives a lower bound of 1.1. Under SGSP, deterministic bounds increase to 1+min{m,n}, with an additional approximation mechanism; randomized lower bounds remain 1.1.\"}]",1784190463,30,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":90,"head_meta":92,"extra_data":94,"updated_unix":27},"mechanism-design-for-locating-a-bridge-between-regions-with-prelocated-facilities","",{"@graph":35,"@context":89},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/mechanism-design-for-locating-a-bridge-between-regions-with-prelocated-facilities/83795/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81,85],{"name":72,"@type":73,"acceptedAnswer":74},"What are agents optimizing after the bridge is built, and how is their cost defined?","Question",{"text":75,"@type":76},"After the bridge is constructed, each agent goes to the nearest prelocated facility in either region. An agent’s cost is the distance from her private location to that nearest facility via the bridge.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which objectives does the paper analyze under strategyproof-type mechanisms?",{"text":80,"@type":76},"It examines both maximum individual cost and total social cost objectives under SP mechanisms, and also under stronger group-strategyproof (GSP) and strong group-strategyproof (SGSP) notions.",{"name":82,"@type":73,"acceptedAnswer":83},"What approximation results are provided under the maximum-cost objective?",{"text":84,"@type":76},"For maximum cost, the paper characterizes the optimal solution satisfying GSP, proposes deterministic 3-approximation and randomized 2-approximation mechanisms under SGSP, and proves a deterministic SGSP lower bound of 2.",{"name":86,"@type":73,"acceptedAnswer":87},"How do the lower bounds differ between deterministic and randomized mechanisms for the social-cost objective?",{"text":88,"@type":76},"For deterministic SP mechanisms, the paper gives a lower bound of 2, while for randomized SP mechanisms it gives a lower bound of 1.1. Under SGSP, deterministic bounds increase to 1+min{m,n}, with an additional approximation mechanism; randomized lower bounds remain 1.1.","https://schema.org",{"og:url":51,"og:type":91,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":93,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":96},[97,101,105,109,114,119,124,126,131,134,138],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},"Exam",70,"exam",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},5,"Comic",60,"comic",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},6,"Technology",50,"technology",{"id":120,"doc_module":4,"doc_module_name":45,"category_name":121,"show_sort_weight":122,"slug":123},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":28,"slug":125},"research-report",{"id":127,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":129,"slug":130},9,"Religion & Spirituality",20,"religion-spirituality",{"id":129,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":129,"slug":133},"World Cup","world-cup",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":135,"slug":137},10,"Lifestyle","lifestyle",{"id":139,"doc_module":4,"doc_module_name":45,"category_name":140,"show_sort_weight":110,"slug":141},19,"General","general"]