Cache-oblivious dynamic programming
Rezaul Chowdhury,Vijaya Ramachandran +1 more
- pp 591-600
TLDR
A new cache-oblivious framework called the Gaussian Elimination Paradigm (GEP) for Gaussian elimination without pivoting that also gives cache-OBlivious algorithms for Floyd-Warshall all-pairs shortest paths in graphs and 'simple DP', among other problems.Abstract:
We present efficient cache-oblivious algorithms for several fundamental dynamic programs. These include new algorithms with improved cache performance for longest common subsequence (LCS), edit distance, gap (i.e., edit distance with gaps), and least weight subsequence. We present a new cache-oblivious framework called the Gaussian Elimination Paradigm (GEP) for Gaussian elimination without pivoting that also gives cache-oblivious algorithms for Floyd-Warshall all-pairs shortest paths in graphs and 'simple DP', among other problems.read more
Citations
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Introduction to computational biology
TL;DR: Tutorial presented at High Performance Computing Center, Stuttgart, Germany.
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Minimizing Communication in Linear Algebra
TL;DR: This work generalizes a lower bound on the amount of communication needed to perform dense, n-by-n matrix multiplication using the conventional O(n3) algorithm to a much wider variety of algorithms, including LU factorization, Cholesky factors, LDLT factors, QR factors, the Gram–Schmidt algorithm, and algorithms for eigenvalues and singular values.
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Minimizing Communication in Numerical Linear Algebra
TL;DR: Hong and Kung as discussed by the authors gave a lower bound on the communication complexity of matrix multiplication in the parallel case. But this lower bound was later extended to a much wider variety of linear algebra algorithms, including LU factorization, Cholesky factorization and LDLT factorization.
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Solving path problems on the GPU
TL;DR: This work implemented a recursively partitioned all-pairs shortest-paths algorithm that harnesses the power of GPUs better than existing implementations and provides evidence that programmers should rethink algorithms instead of directly porting them to GPU.
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Graph expansion and communication costs of fast matrix multiplication
TL;DR: Lower bounds on the communication cost of algorithms are shown to be closely related to the expansion properties of the corresponding computation graphs, and these bounds are attainable both for sequential and for parallel algorithms and hence optimal.
References
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Book
Dynamic Programming
TL;DR: The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.
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Introduction to algorithms: 4. Turtle graphics
TL;DR: In this article, a language similar to logo is used to draw geometric pictures using this language and programs are developed to draw geometrical pictures using it, which is similar to the one we use in this paper.
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What is dynamic programming
TL;DR: Sequence alignment methods often use something called a 'dynamic programming' algorithm, which can be a good idea or a bad idea, depending on the method used.