Yehuda Afek Tel-Aviv University and IDC Herzliya afek@math.tau.ac.il Gideon Stupp Tel-Aviv University stupp@math.tau.ac.il Dan Touitou IBM Research Lab in Haifa Israel dant@il.ibm.com ABSTRACT Long-lived and adaptive to point contention implementations of snapshot and immediate snapshot objects in the read/write shared-memory model are presented. In [2] we presented adaptive algorithms for mutual exclusion, collect and snapshot. However, the collect and snapshot algorithms were adaptive only when the number of local primitive operations that a process performs are ignored, i.e., not counted. The number of primitive local steps (operations that do not access the shared memory) in the collect and snapshot operations presented in [2] is O(Nk ) and O(Nk ) respectively where N is the total number of processes in the system and k is the encountered contention. Here we developed new techniques that enabled us to achieve fully adaptive implementations in which the step complexity (combined local and shared) of any operation is bounded by a function of the number of processes that are concurrent with the operation, in particular, O(k ) for the snapshot implementation.

this paper. Motivated by their first work Moir and Anderson developed renaming algorithms, in the read/write model, when such a bound on the maximum number of processes is known in advance. This led to a sequence of works on the renaming problem in this model [MA95, MG96, BGHM95] that lead to a long-lived (2K \Gamma 1)-renaming algorithm with O(K ) step complexity and O(K space complexity [Moi98]. These works employed various variants of the splitter building block which is a descendant of Lamport's adaptive mutual exclusion algorithm, however the last one [Moi98] depends on an additional work which is the first long-lived renaming algorithm by Burns and Peterson [BP89]