The input/output complexity of sorting and related problems
Communications of the ACM
Efficient out-of-core algorithms for linear relaxation using blocking covers
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
New tiling techniques to improve cache temporal locality
Proceedings of the ACM SIGPLAN 1999 conference on Programming language design and implementation
A survey of out-of-core algorithms in numerical linear algebra
External memory algorithms
Memory characteristics of iterative methods
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Tiling optimizations for 3D scientific computations
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
Tight Bounds on Capacity Misses for 3D Stencil Codes
ICCS '02 Proceedings of the International Conference on Computational Science-Part I
I/O complexity: The red-blue pebble game
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Tight Bounds on Capacity Misses for 3D Stencil Codes
ICCS '02 Proceedings of the International Conference on Computational Science-Part I
Tight bounds for low dimensional star stencils in the external memory model
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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Stencil codes such as the Jacobi, Gau脽-Seidel, and red-black Gau脽-Seidel kernels are among the most time-consuming routines in many scientific and engineering applications. The performance of these codes critically depends on an efficient usage of caches, and can be improved by tiling. Several tiling schemes have been suggested in the literature; this paper gives an overview and comparison. Then, in the main part, we prove a lower bound on the number of cold and capacity misses. Finally, we analyze a particular tiling scheme, and show that it is off the lower bound by a factor of at most six. Our results show up limitations to the speedup that can be gained by future research.