[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82631-en":3,"doc-seo-82631-105":29,"detail-sidebar-cat-0-en-105":90},{"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":4,"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},82631,16904993612988,"Olivia Brown","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Output-Sensitive Construction of CDAWGs from BWT-Runs","Compact directed acyclic word graphs (CDAWGs) for a string are addressed through two equivalent views: edge-compacted DAWGs and suffix-tree-derived DAGs obtained by merging nodes with isomorphic subtrees. The work builds the CDAWG for the reversed input string of length n with eL edges in O(eL log n log(n/r)) time, using O(r log(n/r)+eL) working space. The bound relies on availability of a fully functional compressed suffix tree whose size is O(r log(n/r)), where r is the number of BWT-runs.","arXiv :2607 .0 1636v 1 [ cs .DS] 2 Jul 2026  \nOutput-Sensitive Construction of CDAWGs from  \nBWT-Runs  \nYuta Tsuruzono 1 , Hiroki Arimura 1, and Shunsuke Inenaga2  \n1 Graduate School of IST, Hokkaido University, Sapporo, Japan  \n[arim@ist.hokudai.ac.jp](arim@ist.hokudai.ac.jp)  \n2 Department of Informatics, Kyushu University, Fukuoka, Japan  \n[inenaga.shunsuke.380@m.kyushu-u.ac.jp](inenaga.shunsuke.380@m.kyushu-u.ac.jp)  \nAbstract. The compact directed acyclic word graph (CDAWG) of a string can be viewed in two equivalent ways: as the edge-compacted DAWGof the string, and as the DAG obtained from the suffix tree by merging the nodes whose subtrees are isomorphic. By exploiting these two views in opposite directions, we show how to build, for the (reversed) input string of length n, the CDAWG with eL edges in O (eL logn log(n/r)) time with O (r log(n/r) + eL ) words of working space, provided that the fully functional compressed suffix tree of Gagie, Navarro, and Prezza of size O (r log(n/r)) is available. Here, r denotes the number of BWT-runs of the input string.  \n1 Introduction  \nThe directed acyclic word graph (DAWG) of a string is the smallest automaton recognizing all substrings of the string [4] . Its edge-compacted version is the compact directed acyclic word graph (CDAWG) [5] . Equivalently, the CDAWGcan be obtained from the suffix tree [10] by merging the nodes whose subtrees are isomorphic. This second view is particularly useful algorithmically: a CDAWG node can be identified by a suffix-tree subtree-equivalence class, while its represented strings are maximal repeats [8] . Thus their size can be much smaller than the text length for highly repetitive strings.  \nA second classical ingredient is the Weiner-link structure of the suffix tree [10] . A Weiner link prepends a character to the represented string. Under reversal, such left extensions become ordinary edges in the DAWG of the reversed string.  \nAnother well-studied measure of repetitiveness is the number r of equalletter runs in the Burrows-Wheeler transform (BWT) . The r-index and the fully functional compressed suffix tree of Gagie, Navarro, and Prezza [6] provide suffix-array and suffix-tree functionality in BWT-run bounded space. Nishimoto and Tabei’s r-enum [9] showed that several characteristic substrings, including maximal repeats, can be enumerated in O(r) words of working space by traversing all right-maximal repeats through Weiner links. Kimura and I [7] subsequently reduced the traversal time to O(n) by using the move data structure for constanttime LF-mapping.  \n2 Tsuruzono, Arimura, Inenaga  \nIn this paper, we present an output-sensitive construction of CDAWGs from BWT-run bounded primitives. Since the maximal repeats are the nodes of the CDAWG, our algorithm can be seen as a generalization and extension of the aforementioned r-enum algorithms. Namely, our algorithm starts from the empty string and traverses Weiner links, in the spirit of r-enum. Hard and soft Weiner links play different conceptual roles. A hard Weiner link leads to a right-maximal locus and is therefore the same kind of step that r-enum uses for maximal-repeat discovery; in our setting, it also represents a primary DAWG edge under string reversal. A soft Weiner link, on the other hand, is not needed merely to enumerate maximal repeats, but it is needed for CDAWG construction because it represents a secondary DAWG edge under string reversal. Thus processing soft Weiner links is one essential difference from r-enum. Computationally, both cases are then handled by the same closure routine: for each left extension aw of a maximal repeat, we compute the right closure q =  and then h =  =  by a doubling-then-binary-search procedure on suffix-array intervals. The algorithm uses key (h) as the target key, and equal target keys are merged according to the suffix-tree subtree-equivalence criterion of Narisawa et al. [8] .  \nLet T = $S\\# be the input string, and let r be the number of BWT","cbCaivShxIYvDIl1","https://ap.wps.com/l/cbCaivShxIYvDIl1","pdf",646961,1,13,"English","en",105,"# Introduction\n# Preliminaries","[{\"question\":\"What two equivalent interpretations of a CDAWG does the paper use?\",\"answer\":\"A CDAWG can be seen as the edge-compacted DAWG of the string, or as a DAG derived from the suffix tree by merging nodes whose subtrees are isomorphic.\"},{\"question\":\"What does the parameter r represent in the time and space bounds?\",\"answer\":\"r denotes the number of BWT-runs of the input string, and it controls the size and workspace requirements through the availability of r-index–based primitives.\"},{\"question\":\"How is the CDAWG constructed in relation to Weiner links?\",\"answer\":\"The algorithm traverses Weiner links starting from the empty string. It processes both hard and soft Weiner links differently, where soft links are required for full CDAWG construction under string reversal.\"}]",1784181918,33,{"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":85,"head_meta":87,"extra_data":89,"updated_unix":27},"output-sensitive-construction-of-cdawgs-from-bwt-runs","",{"@graph":35,"@context":84},[36,53,67],{"@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/output-sensitive-construction-of-cdawgs-from-bwt-runs/82631/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What two equivalent interpretations of a CDAWG does the paper use?","Question",{"text":74,"@type":75},"A CDAWG can be seen as the edge-compacted DAWG of the string, or as a DAG derived from the suffix tree by merging nodes whose subtrees are isomorphic.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What does the parameter r represent in the time and space bounds?",{"text":79,"@type":75},"r denotes the number of BWT-runs of the input string, and it controls the size and workspace requirements through the availability of r-index–based primitives.",{"name":81,"@type":72,"acceptedAnswer":82},"How is the CDAWG constructed in relation to Weiner links?",{"text":83,"@type":75},"The algorithm traverses Weiner links starting from the empty string. It processes both hard and soft Weiner links differently, where soft links are required for full CDAWG construction under string reversal.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":105,"slug":137},19,"General","general"]