The input/output complexity of sorting and related problems
Communications of the ACM
I/O complexity: The red-blue pebble game
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Automatic performance tuning of sparse matrix kernels
Automatic performance tuning of sparse matrix kernels
Optimal sparse matrix dense vector multiplication in the I/O-model
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Bioinformatics
The i/o complexity of sparse matrix dense matrix multiplication
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
The efficiency of mapreduce in parallel external memory
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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We consider evaluating one bilinear form defined by a sparse Ny × Nx matrix A having h entries on w pairs of vectors The model of computation is the semiring I/O-model with main memory size M and block size B. For a range of low densities (small h), we determine the I/O-complexity of this task for all meaningful choices of Nx, Ny, w, M and B, as long as M ≥ B2 (tall cache assumption). To this end, we present asymptotically optimal algorithms and matching lower bounds. Moreover, we show that multiplying the matrix A with w vectors has the same worst-case I/O-complexity.