We consider the complexity of join problems, focusing on equijoins, spatial-overlap joins, and set-containment joins.We use a graph pebbling model to characterize these joins combinatorially, by the length of their optimal pebbling strategies and computationally, by the complexity of discovering these strategies. Our results show that equijoins are the easiest of all joins, with optimal pebbling strategies that meet the lower bound over all join problems and that can be found in linear time. By contrast, spatial-overlap and set-containment joins are the hardest joins, with instances where optimal pebbling strategies reach the upper bound over all join problems and with the problem of discovering optimal pebbling strategies being NP-complete. For set-containment joins, we show that discovering the optimal pebbling is also MAX-SNP-Complete. As a consequence, we show that unless NP = P, there is a constant \u000f0, such that this problem cannot be approximated within a factor of 1 + \u000f0 in polynomial time. Our results shed some light on the di\u000efficulty the applied community has had in \ffinding good” algorithms for\u00a0 spatial-overlap and set-containment joins.<\/p>\n","protected":false},"excerpt":{"rendered":"
We consider the complexity of join problems, focusing on equijoins, spatial-overlap joins, and set-containment joins.We use a graph pebbling model to characterize these joins combinatorially, by the length of their optimal pebbling strategies and computationally, by the complexity of discovering these strategies. Our results show that equijoins are the easiest of all joins, with optimal […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Association for Computing Machinery, Inc.","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"PODS","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"Copyright \u00a9 2001 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and\/or a fee. Request permissions from Publications Dept, ACM Inc., fax +1 (212) 869-0481, or permissions@acm.org. The definitive version of this paper can be found at ACM's Digital Library --http:\/\/www.acm.org\/dl\/.","msr_conference_name":"PODS","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Jin Yi Cai, Venkatesan T. Chakaravarthy, Jeffrey F. 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