[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82726-en":3,"doc-seo-82726-105":29,"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":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},82726,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","Optimality-Preserving Data Reduction for Maximum k-Cut","Optimality-Preserving Data Reduction for Maximum k-Cut studies preprocessing strategies that enable exact solvers to handle larger instances of the Maximum k-Cut problem. The work introduces structured cut sets, providing deletion criteria that preserve optimality and decompose the graph into connected components solvable independently, then recombined into an optimal solution. It also extends Maximum Cut preprocessing rules to the k-Cut setting and proves correctness via a new weighted-graph proof framework. A computational framework yields smaller preprocessed instances and substantial speed-ups.","arXiv :2607 .0328 1v 1 [ cs .DS] 3 Jul 2026  \nOptimality-Preserving Data Reduction for Maximum k-Cut (Full Version)  \nMichael Kaibel 1 \\#  University of Bonn, Germany Petra Mutzel \\#  University of Bonn, Germany  \nLamarr Institute, Bonn, Germany  \n~~ Abstract ~~  \nPreprocessing has become an increasingly important part of solving Maximum Cut to optimality, enabling exact solvers to tackle significantly larger instances. This suggests that exact solvers for the more general Maximum k-Cut problem could also benefit from sophisticated preprocessing. However, to the best of our knowledge, no preprocessing techniques that are effective for k ą 2 have been published.  \nIn this paper, we introduce structured cut sets, a novel data reduction technique for Maximum k-Cut. We provide criteria under which deleting cut sets is optimality-preserving, yielding a decomposition into connected components that can be solved independently and whose solutions can be combined into an optimal solution for the original graph. Furthermore, we extend several preprocessing techniques from Maximum Cut to Maximum k-Cut. To show that our rules are optimality-preserving, we develop a new proof framework based on the addition of weighted graphs.  \nWe complement our theoretical results by engineering a preprocessing framework for Maximum k-Cut and show its effectiveness in a computational study. The preprocessed instances are typically significantly smaller. Integrating our preprocessing into an exact solver yields significant speed-upsand enables solving more instances to optimality.  \n2012 ACM Subject Classification Mathematics of computing Ñ Combinatorial optimization; Theory of computation Ñ Network optimization  \nKeywords and phrases Data Reduction, Preprocessing, Maximum k-Cut Digital Object Identifier 10.4230/LIPIcs...  \nSupplementary Material Our source code is publicly available under [https://github.com/mkaibel/](https://github.com/mkaibel/)[ ](https://github.com/mkaibel/)MaxKCutPreprocessing  \nFunding This research was partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grant FOR-5361 – 459420781.  \nAcknowledgements The authors gratefully acknowledge the access to the Marvin cluster and the support provided by the High Performance Computing & Analytics Lab of the University of Bonn  \n 1  Introduction  \nGraph partitioning problems are a fundamental class of optimization problems. A classic example is the Maximum k-Cut problem (Max k-Cut for short), which asks for a partition of the nodes of a graph into up to k subsets, maximizing the sum of weights of edges whose endpoints lie in different sets. An example is illustrated in Figure 1 . The problem is N P-hard, which can be shown with a reduction from the related k-Colouring problem, one of Karp’s 21 NP-complete problems [23] .  \n1 Corresponding author  \n© Michael Kaibel and Petra Mutzel;  \nlicensed under Creative Commons License CC-BY 4.0  \nLeibniz International Proceedings in Informatics  \nSchloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany  \nXX:2 Optimality-Preserving Data Reduction for Maximum k-Cut (Full Version)  \n(a) An instance (b) A suboptimal solution (c) An optimum solution  \n Figure 1 An example of Maximum k-Cut on a unit weight graph with k “ 3. All edges have weight 1. Partitions are encoded by colour.  \nResearch into Max k-Cut has been motivated by its various applications, e.g., in computing relaxations of frequency assignment problems [10], chip load balancing [17, 36], and image reconstruction [8] . Special attention has been placed on the case k “ 2, called Maximum Cut (MaxCut for short) . Recent research has shown that preprocessing can significantly reduce the size of real world instances for MaxCut by locating substructures for which the behaviour of the optimum solution can be determined ahead of time [13, 27 , 3 , 24] . This preprocessing enables exact solvers to tackle significantly larger instances, some","cbCaigOsyFuyj1RZ","https://ap.wps.com/l/cbCaigOsyFuyj1RZ","pdf",1037396,1,31,"English","en",105,"# Introduction\n# Preliminaries\n# Optimality-Preserving Preprocessing Approach\n# Computational Study","[{\"question\":\"What problem does the document address?\",\"answer\":\"The document addresses preprocessing for the Maximum k-Cut problem, aiming to reduce instance size while preserving the ability to reach an optimal solution.\"},{\"question\":\"What is the key technique introduced for data reduction?\",\"answer\":\"It introduces structured cut sets, along with criteria for deleting cut sets so the remaining problem decomposes into independently solvable connected components.\"},{\"question\":\"How is optimality preserved and proven?\",\"answer\":\"Optimality-preserving rules are justified using a new proof framework based on the addition of weighted graphs.\"}]",1784182523,78,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":27},"optimality-preserving-data-reduction-for-maximum-k-cut","",{"@graph":35,"@context":85},[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/optimality-preserving-data-reduction-for-maximum-k-cut/82726/",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],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the document address?","Question",{"text":75,"@type":76},"The document addresses preprocessing for the Maximum k-Cut problem, aiming to reduce instance size while preserving the ability to reach an optimal solution.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the key technique introduced for data reduction?",{"text":80,"@type":76},"It introduces structured cut sets, along with criteria for deleting cut sets so the remaining problem decomposes into independently solvable connected components.",{"name":82,"@type":73,"acceptedAnswer":83},"How is optimality preserved and proven?",{"text":84,"@type":76},"Optimality-preserving rules are justified using a new proof framework based on the addition of weighted graphs.","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":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]