[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82279-en":3,"doc-seo-82279-105":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},82279,13056703019662,"Evangeline","https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188",8,"Research & Report","Matroid Contention Resolution with Concentration","Contention resolution schemes (CRS) are widely used to round fractional solutions under combinatorial constraints, but existing analyses typically ensure only lower bounds on expected value and upper-tail concentration, leaving the lower tail unconstrained. This limits CRS applicability to covering-constraint problems. The work derives dimension-free lower-tail bounds for the AW random-order CRS, using a new strong λ-boundedness property and a sequential selection process framework. Results enable new approximations for covering-constrained matroid intersection coloring and monotone submodular maximization under matroid plus packing/covering constraints.","arXiv :2607 .09268v 1 [ cs .DS] 10 Jul 2026  \nMatroid Contention Resolution with Concentration Stephen Arndt* Benjamin Moseley† Kirk Pruhs‡ Michael Zlatin§  \nAbstract  \nContention resolution schemes (CRS) are a fundamental and widely applied tool for rounding fractional solutions subject to combinatorial constraints. However, the known analyses of CRS generally only guarantee lower bounds on the expected value and concentration on the upper tail, but no concentration on the lower tail. Thus, CRS are generally not applicable to problems that contain covering constraints, since certifying a covering constraint holds requires a lower tail bound.  \nOur main contribution is to derive lower tail bounds for the output of a particular contention resolution scheme, the random-order CRS of Adamczyk and Włodarczyk, which we call AW. We show that every linear function of the rounded solution attains a constant fraction of its expectation with a failure probability that is dimension-free, depending only on the expected value and on the number of matroids, but not on the size of the ground set.  \nOur analysis is driven by a new property we call strong λ-boundedness, which strengthens the known λ-boundedness of AW by providing two-sided control on how rounding propagates between elements. We then introduce a random process capturing AW, a sequential selection process, that may be of independent interest. We prove lower tail bounds for any strongly λ-bounded sequential selection process.  \nTo demonstrate the applicability of our new tail bounds, we apply them to two problems involving covering constraints. The first result is an O(k log k)-approximation for k-matroid intersection coloring (improving the prior O (k2 )) when the chromatic number of at least one matroid is Ω(k3 log n), where n is the number of elements. The second is the first bicriteria approximation algorithm for monotone submodular maximization under k matroid constraints together with packing and covering constraints.  \n1 Introduction  \nRandomized rounding of fractional solutions is one of the most powerful and broadly applicable techniques in the design of approximation algorithms. The foundational work of Raghavan and Thompson [RT87] showed that independent randomized rounding of a fractional solution to a packing or covering LP, combined with Chernoff-Hoeffding concentration bounds, yields near-optimal integral solutions with high probability for a diverse set of problems. This insight sparked a long line of work on dependent randomized rounding, where the rounding procedure introduces carefully designed correlations among the rounded variables in order to enforce additional structural constraints on the output, such as matroid independence, matching feasibility, or knapsack capacity, that independent rounding cannot guarantee. Prominent examples include pipage rounding [AS04], swap rounding [CVZ10], dependent rounding for bipartite graphs [GKPS06], and the rounding schemes implicit in iterated rounding algorithms [LRS11] .  \nA particularly significant development in this line of work was the shift from designing problem-specific rounding algorithms to designing generic rounding frameworks that apply to a family of problems. The contention resolution scheme (CRS) framework introduced by Chekuri, Vondrk and Zenklusen [CVZ14],  \n*Tepper School of Business, Carnegie Mellon University.  \n†Tepper School of Business, Carnegie Mellon University.  \n‡Department of Computer Science, University of Pittsburgh. Supported in part by NSF grant CCF-2209654 .  \n§Department of Computer Science, Pomona College.  \napplies to rounding a polytope P ⊆ [0 , 1]N which is the independence polytope of a down-closed family of subsets I ⊆ 2N .  \nDefinition 1. The input to a Contention Resolution Scheme (CRS) π is a fractional point x ∈ P and a (not necessarily feasible) subset A ⊆ U of elements, and the output is a feasible subset S of both A and the support of x, that is S ⊆ A ∩ support(x) and S ∈ I","cbCaionQMR3nTqII","https://ap.wps.com/l/cbCaionQMR3nTqII","pdf",474509,2,1,36,"English","en",105,"# Abstract\n# Introduction\n## Current Limits to the Applicability of CRS","[{\"question\":\"Why are standard contention resolution schemes difficult to apply to covering-constraint problems?\",\"answer\":\"Known CRS analyses mainly provide lower bounds on expected value and guarantees on the upper tail, but they do not bound the lower tail. Covering constraints require certification that the constraint holds, which in turn depends on having a lower-tail guarantee.\"},{\"question\":\"What is the main new contribution of the paper?\",\"answer\":\"The paper derives lower tail bounds for the output of the random-order CRS of Adamczyk and Włodarczyk (AW). It shows that every linear function of the rounded solution attains a constant fraction of its expectation with a failure probability that is dimension-free.\"},{\"question\":\"What concept enables the new lower-tail analysis?\",\"answer\":\"The analysis is driven by a new property called strong λ-boundedness. It strengthens the known λ-boundedness of AW by giving two-sided control on how rounding propagates between elements, leading to lower-tail guarantees for related sequential selection processes.\"}]",1784179359,91,{"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},"matroid-contention-resolution-with-concentration","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/matroid-contention-resolution-with-concentration/82279/",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","2026-07-21","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},"Why are standard contention resolution schemes difficult to apply to covering-constraint problems?","Question",{"text":75,"@type":76},"Known CRS analyses mainly provide lower bounds on expected value and guarantees on the upper tail, but they do not bound the lower tail. Covering constraints require certification that the constraint holds, which in turn depends on having a lower-tail guarantee.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the main new contribution of the paper?",{"text":80,"@type":76},"The paper derives lower tail bounds for the output of the random-order CRS of Adamczyk and Włodarczyk (AW). It shows that every linear function of the rounded solution attains a constant fraction of its expectation with a failure probability that is dimension-free.",{"name":82,"@type":73,"acceptedAnswer":83},"What concept enables the new lower-tail analysis?",{"text":84,"@type":76},"The analysis is driven by a new property called strong λ-boundedness. It strengthens the known λ-boundedness of AW by giving two-sided control on how rounding propagates between elements, leading to lower-tail guarantees for related sequential selection processes.","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":20,"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"]