[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84532-en":3,"doc-seo-84532-105":30,"detail-sidebar-cat-0-en-105":83},{"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},84532,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Computing Smallest Suffixient Arrays in Sublinear Time","A suffixient array is a compact indexing structure that supports efficient pattern matching on a text T when paired with random access to its representation. This work computes a smallest suffixient array for T[1..n] in O(loglogσ n + min(r,r) logε n) time, where σ is alphabet size and r, r are the numbers of equal-letter runs in the Burrows–Wheeler transform of T and its reverse, respectively. The method yields sublinear time under suitable repetitiveness and alphabet conditions and presents connected algorithmic results.","arXiv :2607 .00204v1 [ cs .DS] 30 Jun 2026  \nComputing Smallest Suffixient Arraysin Sublinear Time  \nHiroto Fujimaru 1 , Gonzalo Navarro2 ,3 , Francisco Olivares2 ,3 , Jakub Radoszewski4 , Giuseppe Romana5 , and Cristian Urbina4  \n1 Department of Information Science and Technology, Kyushu University, Japan [fujimaru.hiroto.134@s.kyushu-u.ac.jp](fujimaru.hiroto.134@s.kyushu-u.ac.jp)  \n2 Department of Computer Science, University of Chile, Chile  \n{gnavarro,[folivares}@uchile.cl](folivares}@uchile.cl)  \n3 Center for Biotechnology and Bioengineering (CeBiB), Chile  \n4 Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland {j.radoszewski,[c.urbina-gallegos}@uw.edu.pl](c.urbina-gallegos}@uw.edu.pl)  \n5 Faculty of Mathematics, University of Palermo, Italy  \n[giuseppe.romana01@unipa.it](giuseppe.romana01@unipa.it)  \nAbstract. A suffixient array is a novel data structure that, when combined with an index providing direct access on a text T , allows us to answer a variety of pattern matching queries. In this work, we show how to  compute a smallest suffixient array for T[1 .. n] in O ( loglogσn + min(r, r)logϵ n) time for any ϵ > 0, where σ is the alphabet size of T and r and r are the numbers of equal-letter runs of the Burrows-Wheeler transforms of T and its reverse T , respectively. This time complexity becomes sublinear when σ is small enough and min(r, r  ) = o( lo~~n~~g~~ϵ ~~n) , yielding an asymptotic improvement over state-of-the-art algorithms. We also present a series of connected algorithmic results.  \nKeywords: Suffixient arrays · Sublinear-time algorithms · BurrowsWheeler transform  \n1 Introduction  \nOne of the most relevant challenges in modern data compression is to represent in compressed space the huge and highly repetitive text collections that naturally arise in fields like Bioinformatics [22,23,31], so as to query them directly in compressed form. To do so, several measures of repetitiveness have been proposed to evaluate the compression effectiveness of those representations [25,26] . Among others, suffixient arrays [11,7] have received much attention in recent years. A suffixient array is a data structure that, once built on a text T[1 .. n], and provided with a representation of T that provides efficient random access toit, can efficiently find one occurrence of P in T , and more generally, of each maximal substring of P that occurs in T (called “maximal exact matches”, or“MEMs”) . This functionality is inferior to that of suffix arrays, but in exchange suffixient arrays can be much smaller on repetitive text collections, and they were  \n2 H. Fujimaru et al.  \nshown to be faster in practice than than other well-known repetitiveness-aware compressed suffix arrays, such as the r-index [14] .  \nMore concretely, the size of a suffixient array is linear in the size of a suffixient set of T , a subset of the positions of T such that any right-extension (i.e., one-character extension of a right-maximal substring) appears aligned at its rightmost position with some suffixient set position [11] . In a way, a suffixient set captures all the different substrings appearing in the text. It is natural then to aim for suffixient sets of minimum cardinality [8], which has been called χ and studied as a repetitiveness measure in its own right [7,27,12,30] .  \nBesides the study of χ, a relevant challenge is how to efficiently find smallest suffixient sets and compute their suffixient arrays (which are the lexicographic order of the reversed prefixes that end at the positions of the suffixient sets) . Cenzato et al. showed how to find smallest suffixient sets in linear time and compressed space [8], and how to test if a given set is suffixient [9] . Other constructions are linear-time online [12], or near-real-time [21] . The smallest suffixient arrays can also be constructed in linear time [5,7] .  \nIn this paper we present the first sublinear-time algorithm to build smallest suffixient arrays under the RA","cbCaishEIvs1wY0z","https://ap.wps.com/l/cbCaishEIvs1wY0z","pdf",693142,3,1,17,"English","en",105,"# Introduction\n## Background and motivation\n## Smallest suffixient sets and arrays\n## Proposed sublinear-time approach","[{\"question\":\"What algorithmic advances are presented?\",\"answer\":\"It provides a new linear-time construction starting from BWT-related structures, then optimizes it for sublinear time using packed representations and modern sublinear-time data structures, with additional implications for approximating χ.\"}]",1784196457,43,{"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":78,"head_meta":80,"extra_data":82,"updated_unix":28},"computing-smallest-suffixient-arrays-in-sublinear-time","",{"@graph":36,"@context":77},[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/computing-smallest-suffixient-arrays-in-sublinear-time/84532/",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","2026-07-20","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"What algorithmic advances are presented?","Question",{"text":75,"@type":76},"It provides a new linear-time construction starting from BWT-related structures, then optimizes it for sublinear time using packed representations and modern sublinear-time data structures, with additional implications for approximating χ.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,127],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]