Summary: ADAPTIVE AND EFFICIENT ALGORITHMS FOR LATTICE
AGREEMENT AND RENAMING \Lambda
HAGIT ATTIYA y AND ARIE FOUREN y
Abstract. In a shared­memory system, n independent asynchronous processes, with distinct
names in the range f0; : : : ; N \Gamma 1g, communicate by reading and writing to shared registers. An
algorithm is wait­free if a process completes its execution regardless of the behavior of other processes.
This paper considers wait­free 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 \Gamma 1)­renaming; the step complexity of both algorithms is O(k log k). An interesting component
of the (6k \Gamma 1)­renaming algorithm is an O(N) algorithm for (2k \Gamma 1)­renaming; this improves on
the best previously known (2k \Gamma 1)­renaming algorithm, which has O(Nnk) step complexity.
The efficient renaming algorithm can be modified into an O(N) implementation of atomic snap­
shots using dynamic single­writer multi­reader registers. The best known implementations of atomic
snapshots have step complexity O(N log N) using static single­writer multi­reader registers, and
O(N) using multi­writer multi­reader registers.
Key words. shared­memory systems, wait­free computation, atomic read/write registers, re­
naming, lattice agreement, atomic snapshots

Source: Attiya, Hagit - Department of Computer Science, Technion, Israel Institute of Technology

Collections: Computer Technologies and Information Sciences