On the cost of recomputing: Tight bounds on pebbling with faults

Yonatan Aumann, Judit Bar-Ilan, Uriel Feige

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We introduce a formal framework to study the time and space complexity of computing with faulty memory. For the fault-free case, time and space complexities were studied using the “pebbling game” model. We extend this model to the faulty case, where the content of memory cells may be erased. The model captures notions such as “check points” (keeping multiple copies of intermediate results), and “recovery” (partial recomputing in the case of failure). Using this model, we derive tight bounds on the time and/or space overhead inflicted by faults. As a lower bound, we exhibit cases where f worst-case faults may necessitate an Ω(f) multiplicative overhead in computation resources (time, space, or their product). The lower bound holds regardless of the computing and recomputing strategy employed. A matching upper-bound algorithm establishes that an O(f) multiplicative overhead always suffices. For the special class of tree computations, we show that faults can be handled with an O(f) additive factor in memory, and only a constant multiplicative overhead in time.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings
EditorsSerge Abiteboul, Eli Shamir
PublisherSpringer Verlag
Pages47-58
Number of pages12
ISBN (Print)9783540582014
DOIs
StatePublished - 1994
Externally publishedYes
EventProceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94 - Jerusalem, Isr
Duration: 1 Jul 19941 Jul 1994

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume820 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceProceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94
CityJerusalem, Isr
Period1/07/941/07/94

Bibliographical note

Publisher Copyright:
© 1994, Springer Verlag. All rights reserved.

Funding

f eige@wisdom, weizmann, ac. il Supported by a Koret Foundation fellowship.

FundersFunder number
Koret Foundation

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