The complexity of robust atomic storage

  • Authors:
  • Dan Dobre;Rachid Guerraoui;Matthias Majuntke;Neeraj Suri;Marko Vukolić

  • Affiliations:
  • TU Darmstadt, Darmstadt, France;EPFL, Lausanne, France;TU Darmstadt, Darmstadt, France;TU Darmstadt, Darmstadt, France;EURECOM, Sophia-Antipolis, France

  • Venue:
  • Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
  • Year:
  • 2011

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Abstract

We study the time-complexity of robust atomic read/write storage from fault-prone storage components in asynchronous message-passing systems. Robustness here means wait-free tolerating the largest possible number t of Byzantine storage component failures (optimal resilience) without relying on data authentication. We show that no single-writer multiple-reader (SWMR) robust atomic storage implementation exists if (a) read operations complete in less than four communication round-trips (rounds), and (b) the time complexity of write operations is constant. More precisely, we present two lower bounds. The first is a read lower bound stating that three rounds of communication are necessary to read from a SWMR robust atomic storage. The second is a write lower bound, showing that Ω(log(t)) write rounds are necessary to read in three rounds from such a storage. Applied to known results, our lower bounds close a fundamental gap: we show that time-optimal robust atomic storage can be obtained using well-known transformations from regular to atomic storage and existing time-optimal regular storage implementations.