Lower bounds on the amortized time complexity of shared objects

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 lockfree 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.