The Impact of Timing on Linearizability in Counting Networks

Counting networks form a new class of distributed, low-contention data structures, made up of interconnected balancers and are suitable for solving a variety of multiprocessor synchronization problems that can be expressed as counting problems. A linearizable counting network guarantees that the order of the values it returns respects the realtime order they were requested. Linearizability signi cantly raises the capabilities of the network, but at a possible price in network size or synchronization support. In this work we further pursue the systematic study of the impact of timing on linearizability for counting networks, along the line of research recently initiated by Lynch et al. in [18]. We consider two basic timing models, the instantaneous balancer model, in which the transition of a token from an input to an output port of a balancer is modeled as an instantaneous event, and the periodic balancer model, where balancers send out tokens at a xed rate. We also consider lower and upper bounds on the delays incurred by wires connecting the balancers. We present necessary and su cient conditions for linearizability in the form of precise inequalities that not only involve timing parameters, but also identify structural parameters of the counting network, which may be of more general interest. Our results extend and strengthen previous impossibility and possibility results on linearizability in counting networks [13, 18]. Department of Informatics, University of Cyprus, Nicosia, CY-1678, Cyprus. ([email protected]) Partially supported by funds for the promotion of research at University of Cyprus (research project \Parallel, Concurrent and Distributed Computations"). Part of the work of this author was performed while visiting Max-Planck Institut f ur Informatik, Saarbr ucken, Germany. Max-Planck-Institut f ur Informatik, Im Stadtwald, 66123 Saarbr ucken, Germany ([email protected]) Correspondingauthor: Max-Planck-Institut f ur Informatik, Im Stadtwald, 66123 Saarbr ucken, Germany. ([email protected]) Tel. (+49)-681-9325122, Fax (+49)-681-9325199