Incremental Calculation for Fully Adaptive Algorithms

The step complexity of fully adaptive (FA) algorithms depends only on the contention during an operation, when counting both local computation and accesses to shared registers. This paper contributes to the design of efficient fully adaptive algorithms by specifying and implementing two generic objects, Gather&f and Collect&f . A Gather&f object returns the value of applying a function f on the information previously stored in the object. In order to reduce the local step complexity, our implementation of a Gather&f calculates f incrementally, as values are stored in the object. This implementation uses only read and write operations on the shared memory. It has O(k) local and shared step complexity for calculating f and O(k) for storing information, where k is the point contention during the operation’s execution interval. A Collect&f further guarantees that the value of f returned by a later collect&f operation does not reflect fewer store operations than a (strictly) earlier collect&f operation. A simple implementation has O(k) local and shared step complexity for calculating f and for storing information. For common applications where collect&f is repeatedly invoked, the paper presents an efficient object called ECollect&f . In this object, storing information takes a single step and calculating f has O(k) local and shared step complexity. To demonstrate the applicability of Gather&f and ECollect&f , we use them to improve the local and shared step complexity of atomic snapshot and immediate snapshot to O(k) and O(k), respectively.