Time and Space Lower Bounds for Implementations Using k-CAS

This paper presents lower bounds on the time- and space-complexity of implementations that use the k compare-and-swap (k-CAS) synchronization primitives. We prove that the use of k-CAS primitives cannot improve neither the time- nor the space-complexity of implementations of widely-used concurrent objects, such as counter, stack, queue, and collect. Surprisingly, the use of k-CAS may even increase the space complexity required by such implementations. We prove that the worst-case average number of steps performed by processes for every n-process implementation of a counter, stack or queue object is Ω(logk+1 n), even if the implementation can use j-CAS for j ≤ k. This bound holds even if a k-CAS operation is allowed to read the k values of the objects it accesses and return these values to the calling process. We also consider more realistic non-reading k-CAS primitives. An operation of a non-reading kCAS primitive is only allowed to return a success/failure indication. For impleme...

• Type: Conference
• Year: 2005
• Where: WDAG
• Authors: Hagit Attiya, Danny Hendler
• Keywords: Algorithms, K-CAS Primitives, Space Complexity, WDAG 2005, Worst-case Average Number