Resilient Dynamic Programming
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- 作者：Saverio Caminiti ; Irene Finocchi ; Emanuele G. Fusco ; Francesco Silvestri
- 关键词：Dynamic programming ; Cache ; oblivious algorithms ; Gaussian Elimination Paradigm ; Memory faults ; Resilient computing
- 刊名：Algorithmica
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：77
- 期：2
- 页码：389-425
- 全文大小：
- 刊物类别：Computer Science
- 刊物主题：Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Inform
- 出版者：Springer US
- ISSN：1432-0541
- 卷排序：77
文摘
We investigate the design of dynamic programming algorithms in unreliable memories, i.e., in the presence of errors that lead the logical state of some bits to be read differently from how they were last written. Assuming that a limited number of memory faults can be inserted at run-time by an adversary with unbounded computational power, we obtain the first resilient algorithms for a broad range of dynamic programming problems, devising a general framework that can be applied to both iterative and recursive implementations. Besides all local dependency problems, where updates to table entries are determined by the contents of neighboring cells, we also settle challenging non-local problems, such as all-pairs shortest paths and matrix multiplication. All our algorithms are correct with high probability and match the running time of their standard non-resilient counterparts while tolerating a polynomial number of faults. The recursive algorithms are also cache-efficient and can tolerate faults at any level of the memory hierarchy. Our results exploit a careful combination of data replication, majority techniques, fingerprint computations, and lazy fault detection. To cope with the complex data access patterns induced by some of our algorithms, we also devise amplified fingerprints, which might be of independent interest in the design of resilient algorithms for different problems.