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Lower Bounds on the Amortized Time Complexity of Shared Objects

Authors Hagit Attiya, Arie Fouren



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Hagit Attiya
Arie Fouren

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Hagit Attiya and Arie Fouren. Lower Bounds on the Amortized Time Complexity of Shared Objects. In 21st International Conference on Principles of Distributed Systems (OPODIS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 95, pp. 16:1-16:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.OPODIS.2017.16

Abstract

The amortized step complexity of an implementation measures its performance as a whole, rather than the performance of individual operations. Specifically, the amortized step complexity of an implementation is the average number of steps performed by invoked operations, in the worst case, taken over all possible executions. The amortized step complexity of a wide range of known lock- free implementations for shared data structures, like stacks, queues, linked lists, doubly-linked lists and binary trees, includes an additive factor linear in the point contention—the number of processes simultaneously active in the execution. This paper shows that an additive factor, linear in the point contention, is inherent in the amortized step complexity for lock-free implementations of many distributed data structures, including stacks, queues, heaps, linked lists and search trees.
Keywords
  • monotone objects
  • stacks and queues
  • trees
  • step complexity
  • remote memory references

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