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EFFICIENT AND ERRORCORRECTING DATA STRUCTURES FOR MEMBERSHIP AND POLYNOMIAL EVALUATION
 SUBMITTED TO THE SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE
"... We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the decoder with high probability either answers correctly or declares “ ..."
Abstract

Cited by 5 (1 self)
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We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the decoder with high probability either answers correctly or declares “don’t know.” Furthermore, if there is no noise on the data structure, it answers all queries correctly with high probability. Our model is the common generalization of an errorcorrecting data structure model proposed recently by de Wolf, and the notion of “relaxed locally decodable codes” developed in the PCP literature. We measure the efficiency of a data structure in terms of its length (the number of bits in its representation), and queryanswering time, measured by the number of bitprobes to the (possibly corrupted) representation. We obtain results for the following two data structure problems: • (Membership) Store a subset S of size at most s from a universe of size n such that membership queries can be answered efficiently, i.e., decide if a given element from the universe is in S. We construct an errorcorrecting data structure for this problem with length nearly linear in s log n that answers membership queries with O(1) bitprobes. This nearly matches the asymptotically optimal parameters for the noiseless case: length O(s log n) and one bitprobe, due to
Dynamic programming in faulty memory hierarchies (cacheobliviously)
, 2011
"... Random access memories suffer from transient errors that lead the logical state of some bits to be read differently from how they were last written. Due to technological constraints, caches in the memory hierarchy of modern computer platforms appear to be particularly prone to bit flips. Since algor ..."
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Cited by 5 (4 self)
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Random access memories suffer from transient errors that lead the logical state of some bits to be read differently from how they were last written. Due to technological constraints, caches in the memory hierarchy of modern computer platforms appear to be particularly prone to bit flips. Since algorithms implicitly assume data to be stored in reliable memories, they might easily exhibit unpredictable behaviors even in the presence of a small number of faults. In this paper we investigate the design of dynamic programming algorithms in faulty memory hierarchies. Previous works on resilient algorithms considered a onelevel faulty memory model and, with respect to dynamic programming, could address only problems with local dependencies. Our improvement upon these works is twofold: (1) we significantly extend the class of problems that can be solved resiliently via dynamic programming in the presence of faults, settling challenging nonlocal problems such as allpairs shortest paths and matrix multiplication; (2) we investigate the connection between resiliency and cacheefficiency, providing cacheoblivious implementations that incur an (almost) optimal number of cache misses. Our approach yields the first resilient algorithms that can tolerate faults at any level of the memory hierarchy, while maintaining cacheefficiency. All our algorithms are correct with high probability and match the running time and cache misses of their standard nonresilient counterparts while tolerating a large (polynomial) number of faults. Our results also extend to Fast Fourier Transform.
Selection in the presence of memory faults, with applications to inplace resilient sorting
 In Proc. 23rd ISAAC, volume 7676 of LNCS
, 2012
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Research Statement
, 2012
"... My main area of research are distributed algorithms in networks. I am particularly interested in the influence of both the amount and the quality of information on the efficiency with which a given task can be performed, in a distributed way. Knowledge available to nodes of the network executing a g ..."
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My main area of research are distributed algorithms in networks. I am particularly interested in the influence of both the amount and the quality of information on the efficiency with which a given task can be performed, in a distributed way. Knowledge available to nodes of the network executing a given algorithm can be partitioned into information provided to them a priori, and information acquired through message exchanges with other nodes. A natural approach to a quantitative study of the impact of information on the efficiency is known in the literature as the advice paradigm. An oracle knowing the network gives a (possibly different) string of bits to each node. Then nodes execute a distributed algorithm that does not assume knowledge of the network, but uses communication between nodes and the advice provided to them by the oracle, in order to complete the task. Thus the framework of advice permits to quantify the minimum amount of information needed for an efficient solution of a given network problem, regardless of the type of information that is provided. On the other hand, the quality of information at the disposal of nodes depends on its accuracy (e.g., how precisely can a node of a sensor network perceive its geographic position) and on its reliability (e.g., how prone to faults are the network components, or how vulnerable to forgery are
Resilient dynamic programming
, 2015
"... 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 runtime by an adver ..."
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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 runtime 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 nonlocal problems, such as allpairs shortest paths and matrix multiplication. All our algorithms are correct with high probability and match the running time of their standard nonresilient counterparts while tolerating a polynomial number of faults. The recursive algorithms are also cacheefficient 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.