{"title":"The input/output complexity of triangle enumeration","authors":"R. Pagh, Francesco Silvestri","doi":"10.1145/2594538.2594552","DOIUrl":"https://doi.org/10.1145/2594538.2594552","url":null,"abstract":"We consider the well-known problem of enumerating all triangles of an undirected graph. Our focus is on determining the input/output (I/O) complexity of this problem. Let E be the number of edges, M<E the size of internal memory, and B the block size. The best results obtained previously are sortE3/2) I/Os (Dementiev, PhD thesis 2006) and O(E2/MB) I/Os (Hu et al., SIGMOD 2013), where sort(n) denotes the number of I/Os for sorting n items. We improve the I/O complexity to O(E3/2/(√MB) expected I/Os, which improves the previous bounds by a factor min(√E/M),√M). Our algorithm is cache-oblivious and also I/O optimal: We show that any algorithm enumerating t distinct triangles must always use Ω(√MB) I/Os, and there are graphs for which t=Ω(E3/2). Finally, we give a deterministic cache-aware algorithm using O(E3/2/√MB) I/Os assuming M > Ec for a constant c > 0. Our results are based on a new color coding technique, which may be of independent interest.","PeriodicalId":302451,"journal":{"name":"Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125543016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Beyond worst-case analysis for joins with minesweeper","authors":"H. Ngo, D. Nguyen, C. Ré, A. Rudra","doi":"10.1145/2594538.2594547","DOIUrl":"https://doi.org/10.1145/2594538.2594547","url":null,"abstract":"We describe a new algorithm, Minesweeper, that is able to satisfy stronger runtime guarantees than previous join algorithms (colloquially ``beyond worst-case'' guarantees) for data in indexed search trees. Our first contribution is developing a framework to measure this stronger notion of complexity, which we call \"certificate complexity,\" that extends notions of Barbay et al. and Demaine et al.; a certificate is a set of propositional formulae that certifies that the output is correct. This notion captures a natural class of join algorithms. In addition, the certificate allows us to define a strictly stronger notion of runtime complexity than traditional worst-case guarantees. Our second contribution is to develop a dichotomy theorem for the certificate-based notion of complexity. Roughly, we show that Minesweeper evaluates $beta$-acyclic queries in time linear in the certificate plus the output size, while for any $beta$-cyclic query, there is some instance that takes superlinear time in the certificate (and for which the output is no larger than the certificate size). We also extend our certificate-complexity analysis to queries with bounded treewidth and the triangle query. We present empirical results that certificates can be much smaller than the input size, which suggests that ideas in minesweeper might lead to faster algorithms in practice.","PeriodicalId":302451,"journal":{"name":"Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122639585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A dynamic I/O-efficient structure for one-dimensional top-k range reporting","authors":"Yufei Tao","doi":"10.1145/2594538.2594543","DOIUrl":"https://doi.org/10.1145/2594538.2594543","url":null,"abstract":"We present a structure in external memory for top-k range reporting, which uses linear space, answers a query in O(lgB n + k/B) I/Os, and supports an update in O(lgB n) amortized I/Os, where n is the input size, and B is the block size. This improves the state of the art which incurs O(lg2B n) amortized I/Os per update.","PeriodicalId":302451,"journal":{"name":"Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems","volume":"41 15","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120887540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Session details: Awards session","authors":"R. Hull, W. Fan, Floris Geerts, Dan Suciu","doi":"10.1145/3255782","DOIUrl":"https://doi.org/10.1145/3255782","url":null,"abstract":"The ACM PODS Alberto O. Mendelzon: test-of-time award 2014","PeriodicalId":302451,"journal":{"name":"Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121669179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}