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

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Automata, Languages and Programming (ICALP 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 820))

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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.

Part of this work was carried out while the author was with the Department of Applied Math., The Weizmann Institute of Science.

Supported by a Koret Foundation fellowship.

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  1. S. Cook. “An Observation on Time-Storage Trade-off”. JCSS 9 (1974), 308–316.

    Google Scholar 

  2. C.E. Hewitt and M.S. Paterson. “Comparative Schematology”. Project MAC Conf. on Concurrent Systems and Parallel Computation, Woods Hole, Mass., 1970, 119–127.

    Google Scholar 

  3. J. Hopcroft, W. Paul, and L. Valiant. “On Time Versus Space”. JACM 24(2), 332–337, 1977.

    Google Scholar 

  4. T. Lengauer and R. E. Tarjan. “Asymptotically tight bounds on time-space tradeoffs in a pebble game”. Journal of the ACM, 29:1087–1130, 1982.

    Google Scholar 

  5. J. von Neumann, and O. Morgenstern. “Theory of games and economic behavior”. Princeton University Press, Princeton, 1944.

    Google Scholar 

  6. M. O. Rabin. ”Efficient Dispersal of Information for Security, Load Balancing and Fault Tolerance”. JACM 36(2):335–348, 1989.

    Google Scholar 

  7. M. O. Rabin. ”The Information Dispersal Algorithm and its Applications”. In Sequences, R. M. Capocelli (Editor), 406–419, Springer-Verlag, 1990.

    Google Scholar 

  8. R. Sethi. “Complete Register Allocation Problems”. SIAM J. Comput., 4 (1975), 226–248.

    Google Scholar 

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Correspondence to Yonatan Aumann .

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Serge Abiteboul Eli Shamir

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© 1994 Springer-Verlag Berlin Heidelberg

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Aumann, Y., Bar-Ilan, J., Feige, U. (1994). On the cost of recomputing: tight bounds on pebbling with faults. In: Abiteboul, S., Shamir, E. (eds) Automata, Languages and Programming. ICALP 1994. Lecture Notes in Computer Science, vol 820. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58201-4

  • Online ISBN: 978-3-540-48566-7

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