Resilient Dynamic Programming

Abstract

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

Engineering a Delegatable and Error-Tolerant Algorithm for Counting Small Subgraphs

“…Conversely, a number of works study algorithms that are resilient to errors but do not in general produce a correctness proof. For example, Caminiti, Finocchi, Fusco, and Silvetri [30] study resilient dynamic programming, Chen, Grigorescy, and de Wolf [33] study error-correcting data structures for membership queries and polynomial evaluation, Cicalese [37] studies fault-tolerant search algorithms, and Finocchi, Grandoni, and Italiano [48] present sorting and searching algorithms robust against memory errors. Herault and Robert [62] review fault-tolerance techniques in high-performance computing, including work on algorithm-based fault tolerance introduced by Huang and Abraham [66].…”