Mahmoud Abo Khamis
Hung Q. Ngo
Christopher Ré
ABSTRACT
We present a simple geometric framework for the relational join. Using this framework, we design an algorithm that achieves the fractional hypertree-width bound, which generalizes classical and recent worst-case algorithmic results on computing joins. In addition, we use our framework and the same algorithm to show a series of what are colloquially known as beyond worst-case results. The framework allows us to prove results for data stored in Btrees, multidimensional data structures, and even multiple indices per table. A key idea in our framework is formalizing the inference one does with an index as a type of geometric resolution; transforming the algorithmic problem of computing joins to a geometric problem. Our notion of geometric resolution can be viewed as a geometric analog of logical resolution. In addition to the geometry and logic connections, our algorithm can also be thought of as backtracking search with memoization.
- S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995. Google Scholar
Digital Library
- M. Abo Khamis, H. Q. Ngo, C. Ré, and A. Rudra. Joins via Geometric Resolutions: Worst-case and Beyond. ArXiv e-prints, Feb. 2015.Google Scholar
- P. Afshani, J. Barbay, and T. M. Chan. Instance-optimal geometric algorithms. In FOCS, pages 129--138, 2009. Google ScholarDigital Library
- N. Alon. On the number of subgraphs of prescribed type of graphs with a given number of edges. Israel J. Math., 38(1--2):116--130, 1981.Google ScholarCross Ref
- S. Arnborg and A. Proskurowski. Linear time algorithms for NP-hard problems restricted to partial k-trees. Discrete Appl. Math., 23(1):11--24, 1989. Google ScholarDigital Library
- A. Atserias, M. Grohe, and D. Marx. Size bounds and query plans for relational joins. In FOCS, pages 739--748. IEEE Computer Society, 2008. Google ScholarDigital Library
- J. Barbay and C. Kenyon. Adaptive intersection and t-threshold problems. In SODA, pages 390--399, 2002. Google ScholarDigital Library
- J. Barbay and C. Kenyon. Alternation and redundancy analysis of the intersection problem. ACM Transactions on Algorithms, 4(1), 2008. Google ScholarDigital Library
- S. Blanas, Y. Li, and J. M. Patel. Design and evaluation of main memory hash join algorithms for multi-core CPUs. In SIGMOD, pages 37--48. ACM, 2011. Google ScholarDigital Library
- S. Chaudhuri. An overview of query optimization in relational systems. In PODS, pages 34--43. ACM, 1998. Google ScholarDigital Library
- C. Chekuri and A. Rajaraman. Conjunctive query containment revisited. Theor. Comput. Sci., 239(2):211--229, 2000. Google ScholarDigital Library
- R. Dechter and J. Pearl. Tree-clustering schemes for constraint-processing. In H. E. Shrobe, T. M. Mitchell, and R. G. Smith, editors, AAAI, pages 150--154. AAAI Press / The MIT Press, 1988.Google Scholar
- R. Dechter and J. Pearl. Tree clustering for constraint networks. Artificial Intelligence, 38(3):353--366, 1989. Google ScholarDigital Library
- E. D. Demaine, A. López-Ortiz, and J. I. Munro. Adaptive set intersections, unions, and differences. In SODA, pages 743--752, 2000. Google ScholarDigital Library
- R. Fagin. Degrees of acyclicity for hypergraphs and relational database schemes. J. ACM, 30(3):514--550, 1983. Google ScholarDigital Library
- R. Fagin, A. Lotem, and M. Naor. Optimal aggregation algorithms for middleware. In Proceedings of the Twentieth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS '01, pages 102--113, New York, NY, USA, 2001. ACM. Google ScholarDigital Library
- E. Friedgut and J. Kahn. On the number of copies of one hypergraph in another. Israel J. Math., 105:251--256, 1998.Google ScholarCross Ref
- A. Gajentaan and M. H. Overmars. On a class of o(n2) problems in computational geometry. Comput. Geom. Theory Appl., 45(4):140--152, May 2012. Google ScholarDigital Library
- G. Gottlob, N. Leone, and F. Scarcello. Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width. J. Comput. Syst. Sci., 66(4):775--808, 2003. Google ScholarDigital Library
- G. Graefe. Query evaluation techniques for large databases. ACM Computing Surveys, 25(2):73--170, June 1993. Google ScholarDigital Library
- M. Grohe and D. Marx. Constraint solving via fractional edge covers. In SODA, pages 289--298. ACM Press, 2006. Google ScholarDigital Library
- M. Gyssens, P. Jeavons, and D. A. Cohen. Decomposing constraint satisfaction problems using database techniques. Artif. Intell., 66(1):57--89, 1994. Google ScholarDigital Library
- M. Gyssens and J. Paredaens. A decomposition methodology for cyclic databases. In Advances in Data Base Theory, pages 85--122, 1982.Google Scholar
- C. Kim, T. Kaldewey, V. W. Lee, E. Sedlar, A. D. Nguyen, N. Satish, J. Chhugani, A. Di Blas, and P. Dubey. Sort vs. hash revisited: fast join implementation on modern multi-core CPUs. Proc. VLDB Endow., 2(2):1378--1389, Aug. 2009. Google ScholarDigital Library
- P. G. Kolaitis and M. Y. Vardi. Conjunctive-query containment and constraint satisfaction. J. Comput. Syst. Sci., 61(2):302--332, 2000. Google ScholarDigital Library
- D. Maier. The Theory of Relational Databases. Computer Science Press, 1983. Google ScholarDigital Library
- D. Marx. Tractable hypergraph properties for constraint satisfaction and conjunctive queries. In STOC, pages 735--744, 2010. Google ScholarDigital Library
- D. Marx. Tractable structures for constraint satisfaction with truth tables. Theory Comput. Syst., 48(3):444--464, 2011. Google ScholarDigital Library
- D. Marx. Tractable hypergraph properties for constraint satisfaction and conjunctive queries. J. ACM, 60(6):42, 2013. Google ScholarDigital Library
- R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon. Network motifs: simple building blocks of complex networks. Science, 298(5594):824--827, October 2002.Google ScholarCross Ref
- H. Q. Ngo, D. T. Nguyen, C. Ré, and A. Rudra. Beyond worst-case analysis for joins with Minesweeper. In PODS, pages 234--245, 2014. Google ScholarDigital Library
- H. Q. Ngo, E. Porat, C. Ré, and A. Rudra. Worst-case optimal join algorithms: {extended abstract}. In PODS, pages 37--48, 2012. Google ScholarDigital Library
- H. Q. Ngo, C. Ré, and A. Rudra. Skew strikes back: New developments in the theory of join algorithms. In SIGMOD RECORD, pages 5--16, 2013. Google ScholarDigital Library
- D. Nguyen, M. Aref, M. Bravenboer, G. Kollias, H. Q. Ngo, C. Ré, and A. Rudra. Join Processing for Graph Patterns: An Old Dog with New Tricks. ArXiv e-prints, 2015.Google ScholarDigital Library
- D. Olteanu and J. Zavodny. Size bounds for factorised representations of query results. ACM Transactions on Database Systems, 2014. To appear. Google ScholarDigital Library
- C. H. Papadimitriou and M. Yannakakis. On the complexity of database queries. In PODS, pages 12--19, 1997. Google ScholarDigital Library
- N. Przulj, D. G. Corneil, and I. Jurisica. Modeling interactome: scale-free or geometric? Bioinformatics, 20(18):3508--3515, 2004. Google ScholarDigital Library
- N. Robertson and P. D. Seymour. Graph minors. II. Algorithmic aspects of tree-width. J. Algorithms, 7(3):309--322, 1986.Google ScholarCross Ref
- F. Scarcello. Query answering exploiting structural properties. SIGMOD Record, 34(3):91--99, 2005. Google ScholarDigital Library
- S. Suri and S. Vassilvitskii. Counting triangles and the curse of the last reducer. In WWW, pages 607--614, 2011. Google ScholarDigital Library
- C. E. Tsourakakis. Fast counting of triangles in large real networks without counting: Algorithms and laws. In ICDM, pages 608--617. IEEE Computer Society, 2008. Google ScholarDigital Library
- J. D. Ullman. Principles of Database and Knowledge-Base Systems, Volume II. Computer Science Press, 1989. Google ScholarDigital Library
- T. L. Veldhuizen. Triejoin: A simple, worst-case optimal join algorithm. In ICDT, pages 96--106, 2014.Google Scholar
- M. Yannakakis. Algorithms for acyclic database schemes. In VLDB, pages 82--94, 1981. Google ScholarDigital Library
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- Joins via Geometric Resolutions: Worst-case and Beyond
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