[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81940-en":3,"doc-seo-81940-105":31,"detail-sidebar-cat-0-en-105":93},{"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":28,"seo_description":14,"update_tm":29,"read_time":30},81940,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","On the Communication Complexity of Maximum Matching and Negative-Weight Shortest Paths","Revisits core graph problems in the deterministic two-party communication model, where the edge set is split between Alice and Bob and the goal is to minimize exchanged bits while solving a global task. Establishes simplified communication protocols based on LP-style reasoning and cutting-plane ideas for maximum matching and shortest paths with negative weights. Highlights new deterministic progress toward efficient maximum matching in general (non-bipartite) graphs, addressing difficulties caused by exponential-size LP formulations.","arXiv :2607 .0575 1v 1 [ cs .DS] 7 Jul 2026  \nOn the Communication Complexity of  \nMaximum Matching and Negative-Weight Shortest Paths Yu Cheng∗ Tianle Jiang† Pachara Sawettamalya‡ Huacheng Yu§  \nAbstract  \nWe revisit several fundamental graph problems in the deterministic two-party communication model. Our main contributions include:  \n• WWVaehzgiliriveaetnhiae[newsamMV8e](n3ppan/ed2r)bG-boaitubprndowoctoan[Gcobable1foo7rb],tcaoomineurpdputbroiytngsociamolmuialatsxincoimgncutemheptmcualaaltcsslyhicsiingalgmpinorilegethannemdras oavl gf Moirdaisphcathlsie-. intricacies of finding a maximal set of shortest augmenting paths.  \n• Wsoaeulogrcnivegeschhaoarintneewstof d(tnhu)sc-btiitOopurnsropwtriocotthoocal fomolrsonimreegpdlatifiireivesctet-cyhatappcleofrodBacetlihecksbttaionadsedeatonandlvne[eBrtgBeatExe2ot-w2e]ebntigyiahrltessplingacileng-• Wgral eap[gihBvsBe,comta22i]bnethindratobyougrirhaelinai(nrpsc)rr-betetiiitnzprgedotthaoenconealylfasiorsr-liconemaprutingcommaumniacxatimumion prmatotoccholinog inf Blbikipstaartidteet  \nTogether, these results provide simpler protocols for several basic graph problems. We hope they will inspire further advances on the communication complexity of a wide range of graph problems.  \n∗ [Brown University.](Brown University. yu_cheng@brown.edu. Supported)[ yu_cheng@brown.edu](Brown University. yu_cheng@brown.edu. Supported)[. Supported](Brown University. yu_cheng@brown.edu. Supported) in part by NSF Award CCF-2307106.  \n†[Duke University.](Duke University. tianle.jiang@duke.edu. Supported)[ tianle.jiang@duke.edu](Duke University. tianle.jiang@duke.edu. Supported)[. Supported](Duke University. tianle.jiang@duke.edu. Supported) in part by NSF Award IIS-2402823 . Part of the work was done while visiting Brown University.  \n‡[Princeton University.](Princeton University. ps3122@princeton.edu. Supported)[ ps3122@princeton.edu](Princeton University. ps3122@princeton.edu. Supported)[. Supported](Princeton University. ps3122@princeton.edu. Supported) in part by NSF CAREER Award CCF-2339942 .  \n§ [Princeton University.](Princeton University. yuhch123@gmail.com. Supported)[ yuhch123@gmail.com](Princeton University. yuhch123@gmail.com. Supported)[. Supported](Princeton University. yuhch123@gmail.com. Supported) in part by NSF CAREER Award CCF-2339942 .  \n1 Introduction  \nGraph theory is central to computer science, both in theory and in practice. The field studies fundamental problems such as connectivity, shortest paths, matching, spanning forests, and cycle detection. Efficient solutions for these problems form the algorithmic backbone of many computational systems. While the complexity of these problems is well understood in centralized models, much less is known when the input is distributed across players with only partial views of the graph.  \nIn this work, we study the communication complexity of graph problems in the standard twoparty model [Yao79] . The edge set of a graph is partitioned between two players, Alice and Bob, who must collaboratively solve a global graph problem while minimizing the amount of communication between them. Although this model is closely related to query, streaming, and distributed models of computation, many fundamental graph problems remain poorly understood from the perspective of communication complexity.  \nA recent breakthrough of Blikstad et al. [BBE+22] showed that maximum bipartite matching an(ndicorastfeievonaseir1ballepAtrreotgbhioleenmcoofsrreaedolfiuctneibhearlierptoapprogitrraadoamcmh(iLtisPd)a)etecuisrmttemiinngpistt-pyiclaopnrrehotfarsocoamnolsewn-uotrsriinkvigtaonestl vlioynglu(nhe)bthThiteisrs ofafrpacoomlmmytopewouerkis particularly well-suited for the two-party edge-partition model: Given a graph problem T, one formulates an LP whose feasibility gives the answer to T, with constraints that are locally checkable and succinctly encodable for communication. The cutting-plane framework is then used to determine the feasibility of this LP, and the result is t","cbCaiad0UYPHutKn","https://ap.wps.com/l/cbCaiad0UYPHutKn","pdf",522236,7,1,28,"English","en",105,"# Introduction\n## Our Contributions\n### Maximum Matching in General Graphs","[{\"question\":\"What communication model does the paper use for graph problems?\",\"answer\":\"It studies the deterministic two-party communication model in which Alice and Bob hold a partition of the graph’s edges and must compute the answer collaboratively while minimizing communication.\"},{\"question\":\"What are the main problem areas addressed?\",\"answer\":\"The focus is on communication complexity for fundamental graph tasks, especially maximum matching and shortest paths in graphs that may contain negative edge weights.\"},{\"question\":\"Why is maximum matching in general graphs harder than in bipartite graphs?\",\"answer\":\"General graphs lack a polynomial-size LP formulation with the same clean duality structure as bipartite matching; the natural primal and dual LPs have exponentially many constraints or variables, making volume/dimension-based analysis difficult.\"}]","On the Communication Complexity of Maximum Matching and Negative-Weight Shortest Paths | PDF",1784177175,71,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":88,"head_meta":90,"extra_data":92,"updated_unix":29},"on-the-communication-complexity-of-maximum-matching-and-negative-weight-shortest-paths","",{"@graph":37,"@context":87},[38,55,70],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/document/research-report/",3,{"item":53,"name":13,"@type":44,"position":54},"https://docshare.wps.com/document/on-the-communication-complexity-of-maximum-matching-and-negative-weight-shortest-paths/81940/",4,{"url":53,"name":13,"@type":56,"author":57,"headline":13,"publisher":59,"fileFormat":62,"inLanguage":24,"description":14,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":42,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-08-03","2026-07-16",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73,79,83],{"name":74,"@type":75,"acceptedAnswer":76},"What communication model does the paper use for graph problems?","Question",{"text":77,"@type":78},"It studies the deterministic two-party communication model in which Alice and Bob hold a partition of the graph’s edges and must compute the answer collaboratively while minimizing communication.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"What are the main problem areas addressed?",{"text":82,"@type":78},"The focus is on communication complexity for fundamental graph tasks, especially maximum matching and shortest paths in graphs that may contain negative edge weights.",{"name":84,"@type":75,"acceptedAnswer":85},"Why is maximum matching in general graphs harder than in bipartite graphs?",{"text":86,"@type":78},"General graphs lack a polynomial-size LP formulation with the same clean duality structure as bipartite matching; 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