[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-290292-105":59,"doc-detail-290292-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","fast-computation-of-sparse-datacubes","Fast Computation of Sparse Datacubes","","Datacube queries compute aggregate views over relations at multiple granularities and are central to decision-support workloads. Real-world data is often sparse, making efficient aggregation over large sparse relations critical. Existing methods do not scale well when the number of CUBE BY attributes grows, especially when the relation size exceeds main memory. A new algorithm is proposed for fast datacube computation on sparse relations, evaluated on synthetic, benchmark, and real datasets.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/fast-computation-of-sparse-datacubes/290292/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/fast-computation-of-sparse-datacubes/290292.png","ImageObject",300,407,{"name":92,"@type":93},"Miles","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What problem do datacube queries address in decision support systems?","Question",{"text":113,"@type":114},"They compute aggregates over a relation at multiple granularities, producing a structured set of results across the dimensions defined by CUBE BY attributes.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Why are sparse datacube computations difficult with existing techniques?",{"text":118,"@type":114},"Existing methods scale poorly with the number of CUBE BY attributes, particularly when the relation is much larger than main memory.",{"name":120,"@type":111,"acceptedAnswer":121},"How does the proposed approach handle cases where the relation does not fit in memory?",{"text":122,"@type":114},"It uses a divide-and-conquer strategy that splits the datacube computation into multiple sub-datacubes, where many subproblems can be computed in memory.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},290292,1789641253,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144,"preview_page_count":4},13056703019404,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Kenneth A.Ross*  \nColumbia University  \nkar@cs.columbia.edu  \n# Abstract\n\nDatacube queries compute aggregates overdatabase relations at a variety of granularities,and they constitute an important class of decisionsupport queries.Real-world data is frequentlysparse,and hence efficiently computing datacubesover large sparse relations is important.We showthat current techniques for computing datacubesover sparse relations do not scale well with thenumber of CUBE BY attributes,especially when therelation is much larger than main memory.  \nWe propose a novel algorithm for the fast com-putation of datacubes over sparse relations,anddemonstrate the efficiency of our algorithm usingsynthetic,benchmark and real-world data sets.When the relation fits in memory,our techniqueperforms multiple in-memory sorts,and does notincur any I/O beyond the input of the relationand the output of the datacube itselfWhenthe relation does not fit in memory,a divide-and-conquer strategy divides the problem of com-puting the datacube into several simpler compu-tations of sub-datacubes.Often,all but one ofthe sub-datacubes can be computed in memoryand our in-memory solution applies.In that case,the total I/O overhead is linear in the number ofCUBE BY attributes.We demonstrate with an im-plementation that the CPU cost of our algorithmis dominated by the I/O cost for sparse relations.  \n# Fast Computation of Sparse Datacubes\n\nDivesh Srivastava  \nAT&T Labs-Researchdivesh@research.att.com  \n## 1 Introduction\n\nDatacube queries compute aggregates over relations at avariety of granularities,and they constitute an importantclass of decision support queries.The databases may rep-resent business data(such as point-of-sales transactions),medical data(such as patient treatments and outcomes),or scientific data(such as large sets of experimental mea-surements).An example datacube query is“Broken downby supplier,part and month,find the total sales in 1996,including all subtotals across each dimension.”  \nThe attributes constituting the dimensions along whichthe aggregates are computed are called CUBE BY attributes.In the query above,for example,the CUBE BY attributes aresupplier,part and month.  \nA relation is sparse with respect to a set of attributesif its cardinality is a small fraction of the size of the cross-product of the attribute domains.We are particularly in-terested in relations that are sparse with respect to theCUBE BY attributes for a given datacube query;when theattributes are understood from the context we will simplyrefer to the relation as sparse.  \nSparseness exists for two distinct reasons:large domainsizes of some CUBE BY attributes and a large number ofCUBE BY attributes in the datacube query.  Real-worlddata in application domains is often very large and sparse.Hence,efficiently computing datacubes over large sparserelations is important.Thc contributions of this paper aredescribed below.  \nWe show that current techniques for computing dat-acubes are not very efficient for sparse relations,especiallywhen the database relation is much larger than main mem-ory(Section 2).  \nWe propose a novel algorithm,Partitioned-Cube,forthe fast computation of datacubes over large sparse rela-tions(Section 3).Partitioned-Cube uses a divide-and-conquer strategy that divides the problem of computingthe datacube over a relation with T tuples and k CUBE BYattributes into n+1 sub-datacubes,for a large number  \nn.The first n of these sub-datacubes each has approx-imately T/n tuples and k CUBE BY attributes.The finalsub-datacube has no more than T tuples and has k-1CUBE BY attributes.  \nWe formulate an algorithm,Memory-Cube,for the effi-cient computation of datacubes over relations that fit inmemory(Section 4).Memory-Cube performs multiple in-  \n\n| SELECT B₁,…,B,G(A)  \u003Cbr>R  \u003Cbr>FROM  \u003Cbr>CUBE BY B₁,.,B   |\n| --- |\n\nFigure 1:Datacube Query Q  \nmemory sorts,and does not incur any I/O beyond the in-put of the relation and the output of the datacube itself.Memory-Cube perfo","cbCaifenwvuisOiw","https://ap.wps.com/l/cbCaifenwvuisOiw","pdf",1210252,"English","# Abstract\n# Fast Computation of Sparse Datacubes\n## 1 Introduction\n## 2 Motivation: Existing Techniques","[{\"question\":\"What problem do datacube queries address in decision support systems?\",\"answer\":\"They compute aggregates over a relation at multiple granularities, producing a structured set of results across the dimensions defined by CUBE BY attributes.\"},{\"question\":\"Why are sparse datacube computations difficult with existing techniques?\",\"answer\":\"Existing methods scale poorly with the number of CUBE BY attributes, particularly when the relation is much larger than main memory.\"},{\"question\":\"How does the proposed approach handle cases where the relation does not fit in memory?\",\"answer\":\"It uses a divide-and-conquer strategy that splits the datacube computation into multiple sub-datacubes, where many subproblems can be computed in memory.\"}]","Fast Computation of Sparse Datacubes | PDF",25]