Linear-time snapshot implementations in unbalanced systems

Anatomic snapshot memory object in shared memory systems enables a set of processes, calledscanners, to obtain a consistent picture of the shared memory while other processes, calledupdaters, keep updating memory locations concurrently. In this paper we present two conversion methods of snapshot implementations. Using the first conversion method we obtain a new snapshot implementation in which the scan operation has linear time complexity and the time complexity of the update operation becomes the sum of the time complexities of the original implementation. Applying the second conversion method yields similar results, where in this case the time complexity of the update protocol becomes linear. Although our conversion methods use unbounded space, their space complexity can be bounded using known techniques. One of the most intriguing open problems in distributed wait-free computing is the existence of a linear-time implementation of this object. Using our conversion methods and known constructions we obtain the following results:

?Consider a system ofn processes, each an updater and a scanner. We present an implementation in which the time complexity of either the update or the scan operation is linear, while the time complexity of the second operation isO(n logn).

?We present an implementation with linear time complexity when the number of either updaters or scanners isO(n/logn), wheren is the total number of processes.

?We present an implementation with amortized linear time complexity when one of the protocols (either upate or scan) is executed significantly more often than the other protocol.