[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84082-en":3,"doc-seo-84082-105":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},84082,1099514067415,"Rowan","https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502",8,"Research & Report","Load Balancing under Adaptive Bin Deletions","Load balancing is studied via a balls-and-bins process against an adaptive adversary that deletes one bin per step and forces the algorithm to redistribute its balls to remaining bins. After n/2 rounds, uniform random redistribution achieves optimal O(n) total recourse and O(log n) maximum load. Using the “power of two choices” reduces the maximum load to O(log log n) while keeping linear recourse. A variant partitions deleted-bin balls evenly into d random bins; d=1 can fail adaptively, while d=2 suffices to recover efficient adaptive balancing.","arXiv :2607 .062 1 1v 1 [ cs .DS] 7 Jul 2026  \nLoad Balancing under Adaptive Bin Deletions  \nHaim Kaplan†,* Shay Sapir‡,* Uri Stemmer†,*  \nAbstract  \nWe analyze a balls-and-bins game against an adaptive adversary that sequentially deletes bins. Starting with n balls distributed across n bins, the adversary deletes a bin in each step, forcing the algorithm to redistribute its balls to surviving bins. We prove that after n/2 rounds, uniform random redistribution yields optimal O (n) recourse and O ( lolog~~ ~~ng~~ ~~logn ) maximum load. Furthermore, we show that applying the “power of two choices” reduces the maximum load to O(log log n) while maintaining linear recourse.  \nWe also consider a variation of this game where the balls from the deleted bin are partitioned evenly among d ≪ n random bins rather than being redistributed independently. We demonstrate that keeping the balls together (d = 1), which gives small maximum load and recourse against an oblivious adversary, fails against an adaptive adversary. Nevertheless, we show that splitting the balls into just two groups (d = 2) is sufficient to recover linear recourse and efficient load balancing in the adaptive setting.  \n1 Introduction  \nBalls-and-bins processes serve as a fundamental abstraction for studying load balancing problems, with diverse applications across numerous domains [ABK94 , KLL + 97 , RS98 , MU05 , Wie07 , FFGM07 , WDL+ 09] . In the simplest version of the problem, n balls are assigned to n bins. Here it is well established that distributing every ball independently and uniformly over the bins yields a maximum load of O ( lolog~~ ~~ng~~ ~~logn )[Gon81] . Furthermore, utilizing the “power of two choices”, where balls are placed sequentially in the least loaded of two randomly chosen bins, dramatically reduces the maximum load to O(log log n) [ABKU99] .  \nBeyond these classical settings, the landscape of balls-and-bins problems is vast. Variations include settings with weighted balls [BFHM08 , PTW10], heterogeneous bin capacities [BBFN14 , Wie07], and graphbased constraints where balls can probe only specific subsets of bins [KP06 , God08] . Berenbrink et al. [BCSV00 , BCSV06] extended the power of two choices from the lightly-loaded case studied by [ABKU99], where the number of balls m is equal to the number of bins n, to the heavily-loaded case, where m ≫ n. Remarkably, they showed that the additive gap between the maximum load and the average load remains the same as in the lightly-loaded case. Los and Sauerwald [LS22] analyzed the power of two choices in an “incomplete information” setting, investigating scenarios where algorithms must rely on load estimates rather than exact values. Vöcking [Vöc03] considered multiple-choice settings (rather than just two choices), where balls areplaced in the least loaded of d selected bins, demonstrating that a nonuniform selection of the d locations leads to better load balancing.  \nOf particular relevance to our work are dynamic variations of balls-and-bins, where the goal is to maintain a balanced allocation over time as balls or bins arrive and depart. This line of work was initiated by [ABKU99], who considered a model where balls are added and deleted at random. They showed that their“power of two choices” extends to this dynamic setting, maintaining a maximum load of O(log log n) in the lightly-loaded case. Subsequent works [CFM+ 98 , Vöc03 , BK22] generalized this to the heavily-loaded case. Furthermore, these works allowed the sequence of operations to be determined by an oblivious adversary, that is, an adversary that fixes the full sequence of ball insertions and deletions before the process begins. Note that the random case studied by [ABKU99] is a special instance of an oblivious adversary.  \n* Google Research †Tel Aviv University ‡Weizmann Institute of Science  \nAdaptive adversary. Unlike an oblivious adversary, who commits to the sequence of operations before the game begins, an adaptive adversary cho","cbCaiaTzMeyaLinZ","https://ap.wps.com/l/cbCaiaTzMeyaLinZ","pdf",678895,3,1,22,"English","en",105,"# Abstract\n# Introduction\n## Adaptive adversaries in dynamic balls-and-bins\n## Related work and dynamic variants","[{\"question\":\"What model does the paper analyze?\",\"answer\":\"The paper studies a balls-and-bins game where an adaptive adversary deletes one bin in each step, and balls in the deleted bin must be redistributed to the surviving bins.\"},{\"question\":\"What performance guarantees are proven for uniform redistribution?\",\"answer\":\"After n/2 rounds, uniform random redistribution gives optimal O(n) recourse and O(log n) maximum load.\"},{\"question\":\"How does the “power of two choices” affect the maximum load?\",\"answer\":\"Applying the power of two choices reduces the maximum load to O(log log n) while maintaining linear recourse in the adaptive setting.\"}]",1784192597,55,{"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},"load-balancing-under-adaptive-bin-deletions","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"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":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/load-balancing-under-adaptive-bin-deletions/84082/",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","2026-07-27","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 model does the paper analyze?","Question",{"text":75,"@type":76},"The paper studies a balls-and-bins game where an adaptive adversary deletes one bin in each step, and balls in the deleted bin must be redistributed to the surviving bins.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What performance guarantees are proven for uniform redistribution?",{"text":80,"@type":76},"After n/2 rounds, uniform random redistribution gives optimal O(n) recourse and O(log n) maximum load.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the “power of two choices” affect the maximum load?",{"text":84,"@type":76},"Applying the power of two choices reduces the maximum load to O(log log n) while maintaining linear recourse in the adaptive setting.","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":47,"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"]