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.

This paper studies the step complexity of adaptive algorithms using primitives stronger than reads and writes. We first consider unconditional primitives, like fetch&inc, which modify the value of the register to which they are applied, regardless of its current value. Unconditional primitives admit snapshot algorithms with O(log(k)) step complexity, where k is the total or the point contention. These algorithms combine a renaming algorithm with a mechanism for propagating values so they can be quickly collected. When only conditional primitives, e.g., compare&swap or LL/SC, are used (in addition to reads and writes), we show that any collect algorithm must perform Omega(k) steps, in an execution with total contention k in O(log(log(n))). The lower bound applies for snapshot and renaming, both one-shot and long-lived. Note that there are snapshot algorithms whose step complexity is polylogarithmic in n using only reads and writes, but there are no adaptive algorithms whose step complexity is polylogarithmic in the contention, even when compare&swap and LL/SC are used.

This article introduces the sieve , a novel building block that allows to adapt to the number of simultaneously active processes (the point contention ) during the execution of an operation. We present an implementation of the sieve in which each sieve operation requires O ( k log k ) steps, where k is the point contention during the operation.The sieve is the cornerstone of the first wait-free algorithms that adapt to point contention using only read and write operations. Specifically, we present efficient algorithms for long-lived renaming, timestamping and collecting information.

In a shared-memory system, n independent asynchronous processes, with distinct names in the range {0, ..., N-1}, communicate by reading and writing to shared registers. An algorithm is wait-free if a process completes its execution regardless of the behavior of other processes. This paper considers wait-free algorithms whose complexity adjusts to the level of contention in the system: An algorithm is adaptive (to total contention) if its step complexity depends only on the actual number of active processes, k; this number is unknown in advance and may change in different executions of the algorithm. Adaptive algorithms are presented for two important decision problems, lattice agreement and (6k-1)-renaming; the step complexity of both algorithms is O(k log k). An interesting component of the (6k-1)-renaming algorithm is an O(N) algorithm for (2k-1)-renaming; this improves on the best previously known (2k-1)-renaming algorithm, which has O(Nnk) step complexity. The efficient renaming algorithm can be modified into an O(N) implementation of atomic snapshots using dynamic single-writer multi-reader registers. The best known implementations of atomic snapshots have step complexity O(N log N) using static single-writer multi-reader registers, and O(N) using multi-writer multi-reader registers.

) Hagit Attiya and Arie Fouren Department of Computer Science The Technion, Haifa 32000, Israel Abstract This paper considers wait-free algorithms whose complexity is constant in the absence of contention, and grows gradually as the number of active processes increases. An algorithm is fast if its complexity depends on the maximal number of active processes, K, and not on the total number of processes in the system, n. An algorithm is adaptive if its complexity depends only on the actual number of active processes, k, which is unknown in advance and may change in different executions of the algorithm. It is shown that two important decision problems, lattice agreement and renaming with linear name space, have adaptive solutions using only read and write operations. An O(k log k) adaptive algorithm for lattice agreement and an O(k log k) adaptive algorithm for (6k \\Gamma 1)-renaming are presented. These algorithms are constructed from several subalgorithms, which are interesting in t...