Adaptive and Efficient Algorithms for Lattice Agreement and Renaming

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.