Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The input/output complexity of sorting and related problems
Communications of the ACM
Rectangular matrix multiplication revisited
Journal of Complexity
Quasilinear algorithms for processing relational calculus expressions (preliminary report)
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Fast rectangular matrix multiplication and applications
Journal of Complexity
Efficient processing of relational calculus expressions using range query theory
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
Fast sparse matrix multiplication
ACM Transactions on Algorithms (TALG)
Scalable computation of acyclic joins
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Algorithms for acyclic database schemes
VLDB '81 Proceedings of the seventh international conference on Very Large Data Bases - Volume 7
Better size estimation for sparse matrix products
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Compressed matrix multiplication
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Improved output-sensitive quantum algorithms for Boolean matrix multiplication
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Matrix chain multiplication via multi-way join algorithms in MapReduce
Proceedings of the 6th International Conference on Ubiquitous Information Management and Communication
Compressed matrix multiplication
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
Exploiting inter-operation parallelism for matrix chain multiplication using MapReduce
The Journal of Supercomputing
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Computing an equi-join followed by a duplicate eliminating projection is conventionally done by performing the two operations in serial. If some join attribute is projected away the intermediate result may be much larger than both the input and the output, and the computation could therefore potentially be performed faster by a direct procedure that does not produce such a large intermediate result. We present a new algorithm that has smaller intermediate results on worst-case inputs, and in particular is more efficient in both the RAM and I/O model. It is easy to see that join-project where the join attributes are projected away is equivalent to boolean matrix multiplication. Our results can therefore also be interpreted as improved sparse, output-sensitive matrix multiplication.