Asynchronous algorithms for shared memory machines

In an effort to develop more realistic models of computation, we introduce several asynchronous shared memory machines and design asynchronous algorithms for those machines. We first model asynchronous protocols for communication across unreliable channels using finite-state machines communicating via an unreliable shared memory. We establish lower bounds on the size of machines and the number of symbols in the transmission alphabet required to achieve reliable communication. We consider two types of finite-state machines and two fault models for the shared memory. In each case, we show that there are robust protocols for deletion and insertion errors. We also show that there are no robust protocols for mutation errors. In contrast, in the synchronous case, robust protocols exist for all of these types of errors.The Parallel Random Access Machine (PRAM) is a fundamental model of parallel computation, but it is not physically realizable. We introduce a more realistic model of parallel computation, the Asynchronous PRAM (APRAM). Let G be a graph with n vertices and m edges. We present two APRAM models and algorithms to find the connected components of G for each model. Algorithm I runs on an APRAM with only atomic read and write primitives and requires O(n log n) rounds. Algorithms II and III run on an APRAM with limited read-modify-write primitives and require O(log n) rounds. Algorithm III is more efficient than Algorithm II and requires fewer global synchronizations. All three algorithms use m + n processors. We then modify our APRAM connected components algorithms to obtain APRAM algorithms for finding a spanning forest or a minimum spanning forest of G.Finally, we present an APRAM algorithm for finding the biconnected components of a connected graph G. Our biconnected components algorithm runs on an APRAM with limited read-modify-write primitives and requires O(log n) rounds using O(m + n) processors