[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117731-en":3,"doc-seo-117731-105":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":4,"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":27,"seo_description":14,"update_tm":28,"read_time":29},117731,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Learning-Based Approaches for Graph Problems - A Survey","Learning-Based Approaches for Graph Problems - A Survey reviews how machine learning frameworks have been used to address classic graph problems, many of which are NP-complete. It contrasts traditional exact, approximate, and heuristic methods by highlighting their limitations in discovering patterns within graph-structured data. The survey systematically analyzes major proposed learning-driven frameworks, discusses their design and performance, and outlines potential research directions, providing a clear entry point for further study.","arXiv :2204 .01057v2 [math .CO] 17 Apr 2022  \nLearning-Based Approaches for Graph Problems: A  \nSurvey  \nKai Siong Yow∗and Siqiang Luo†  \nSchool of Computer Science and Engineering, College of Engineering, Nanyang Technological University, Singapore  \nApril 19, 2022  \nAbstract  \nOver the years, many graph problems speci􀀌cally those in NP-complete are studied by a wide range of researchers. Some famous examples include graph colouring, travelling salesman problem and subgraph isomorphism. Most of these problems are typically addressed by exact algorithms, approximate algorithms and heuristics. There are however some drawback for each of these methods. Recent studies have employed learning-based frameworks such as machine learning techniques in solving these problems, given that they are useful in discovering new patterns in structured data that can be represented using graphs. This research direction has successfully attracted a considerable amount of attention. In this survey, we provide a systematic review mainly on classic graph problems in which learning-based approaches have been proposed in addressing the problems. We discuss the overview of each framework, and provide analyses based on the design and performance of the framework. Some potential research questions are also suggested. Ultimately, this survey gives a clearer insight and can be used as a stepping stone to the research community in studying problems in this 􀀌eld.  \nKeywords: graph algorithm, graph optimisation, graph problem, NP-complete problem, learning-based approach, machine learning  \n1 Introduction  \nA graph G = (V, E) is a non-linear data structure that contains of a set of vertices (or nodes) V and a set of edges (or links) E. Edges can either be undirected or  \n∗ Email: [kaisiong.yow@ntu.edu.sg](kaisiong.yow@ntu.edu.sg) (The author is currently on Leave of Absense from the Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia.)  \n†Email: [siqiang.luo@ntu.edu.sg](siqiang.luo@ntu.edu.sg)  \ndirected, and a symbolic label or a numeric attribute could be associated with each edge in a graph. Graphs can be used to model many aspects in daily life including transportation system, connectivity of the World Wide Web, social networks and scheduling.  \nKarp [77] showed that there are 21 combinatorial and graph theoretical problems that can be reduced to the boolean satis􀀌ability problem in polynomial time based on Cook’s theorem [31], which implies that these problems are all NP-complete. Out of the 21 problems, ten are decision versions of graph optimisation problems whereas others can be formulated on graphs. Some well known NP-complete problems include 3-satis􀀌ability (3-SAT), clique, vertex cover, graph colouring and partition. More NPcomplete problems can also be found in [50] . Due to the nature of these problems, the time required to solve them grows exponentially to the size of the problems, by using any of the currently known algorithm.  \nGenerally, most of the NP-hard graph optimisation problems are tackled by exact algorithms, approximate algorithms and heuristic. Exact algorithms usually solve a problem to optimality based on integer programming. However, they are not suitable in handling large instances due to the scalability issues. Approximate algorithms are generally used to approximate optimal solutions in polynomial time. However, they may not output the exact solutions but only solutions with weak optimality guarantees (which may not even exist sometimes) . To solve problems in a more e􀀎cient manner, heuristic techniques that sacri􀀌ce optimality and accuracy are designed. They are often lack of theoretical guarantees and requires substantial problem-speci􀀌c research. Since similar combinatorial structures are used to solve the same type of problems, learning-based approaches are introduced in addressing combinatorial optimisation problems in NP-complete.  \nMachine learning (ML) [100 , 7] is one of the arti􀀌ci","cbCaisRSC6Ws0dqp","https://ap.wps.com/l/cbCaisRSC6Ws0dqp","pdf",430314,1,40,"English","en",105,"# Introduction\n## Graph problems and NP-completeness\n## Traditional solution methods\n## Machine learning for graph optimization\n## Learning paradigms: supervised, unsupervised, semi-supervised, reinforcement learning","[{\"question\":\"Which graph problems does the survey focus on?\",\"answer\":\"The survey focuses on classic graph problems where learning-based approaches have been proposed, with many examples connected to NP-complete complexity.\"},{\"question\":\"How do traditional algorithms typically solve NP-complete graph problems?\",\"answer\":\"Exact algorithms aim for optimal solutions via methods like integer programming; approximate algorithms aim for near-optimal solutions with polynomial-time runtimes; heuristics trade optimality and accuracy for efficiency.\"},{\"question\":\"What role does machine learning play in solving graph problems?\",\"answer\":\"Machine learning uses available data to discover patterns in graph-structured inputs and to make predictions or improve performance, enabling approaches for NP-hard graph optimization problems.\"}]","Learning-Based Approaches for Graph Problems - A Survey | PDF",1785679262,101,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"learning-based-approaches-for-graph-problems-a-survey","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"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/learning-based-approaches-for-graph-problems-a-survey/117731/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Which graph problems does the survey focus on?","Question",{"text":75,"@type":76},"The survey focuses on classic graph problems where learning-based approaches have been proposed, with many examples connected to NP-complete complexity.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do traditional algorithms typically solve NP-complete graph problems?",{"text":80,"@type":76},"Exact algorithms aim for optimal solutions via methods like integer programming; approximate algorithms aim for near-optimal solutions with polynomial-time runtimes; heuristics trade optimality and accuracy for efficiency.",{"name":82,"@type":73,"acceptedAnswer":83},"What role does machine learning play in solving graph problems?",{"text":84,"@type":76},"Machine learning uses available data to discover patterns in graph-structured inputs and to make predictions or improve performance, enabling approaches for NP-hard graph optimization problems.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"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":21,"slug":118},7,"Healthcare","healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]