Long-Lived Snapshots with Polylogarithmic Amortized Step Complexity

Abstract

We present the first deterministic wait-free long-lived snapshot algorithm, using only read and write operations, that guarantees polylogarithmic amortized step complexity in all executions. This is the first non-blocking snapshot algorithm, using reads and writes only, that has sub-linear amortized step complexity in executions of arbitrary length. The key to our construction is a novel implementation of a 2-component max array object which may be of independent interest. CCS Concepts: • Theory of computation → Concurrent algorithms.

Upper and Lower Bounds for Deterministic Approximate Objects

“…Then, by extension of the lower bound of Attiya and Hendler, [16], we prove that any n-process solo-terminating implementation of a k-multiplicative-accurate counter from read/write and conditional primitive operations (including kword compare-and-swap) has amortized step complexity of Ω(log(n/k 2 )), for k ≤ √ n/2. Our results together with the upper and lower bound on exact counting proved in [9] show that when the approximation parameter k does not depend on n, relaxing the counter semantics by allowing a multiplicative error cannot asymptotically reduce the amortized step complexity by more than a logarithmic factor.…”

“…In [9] Baig et al present the first wait-free read/write exact counter whose amortized step complexity is polylogarithmic in n, O(log 2 n), in executions of arbitrary length and prove that their algorithm is optimal in terms of amortized step complexity up to a logarithmic factor.…”

“…The exact max register object has been proposed in [8] where Aspnes et al present a bounded variant of this object to beat the linear lower bound on the worst case step complexity by Jayanti et al In particular, their algorithm has O(log m) worst case step complexity for both Read () and Write(v ) operations provided that the value written in the max register does not exceed the value m. Their algorithm is optimal [5]. Baig et al [9] presented an unbounded deterministic max register implementation with polylogarithmic amortized step complexity in executions of arbitrary length.…”

An Efficient Adaptive Partial Snapshot Implementation

“…Aspnes, Attiya, Censor-Hillel, and Ellen [6] proved that it is possible to break through this barrier by restricting the number of operations. They implemented a deterministic algorithm that has worst-case step complexity of O(log 3 n), as long as the number of operations on the object is polynomial in n. Subsequently, Aspnes and Censor-Hillel, gave a randomized algorithm with poly-logarithmic expected step complexity [7], and Ahad Baig, Hendler, Milani, and Travers devised a deterministic algorithm with poly-logarithmic amortized worst-case step complexity [10].…”

“…10. Suppose process p executes an Update() operation up and inserts a pair (key, v) into versions[p] in line 25.…”