Electing an Eventual Leader in an Asynchronous Shared Memory System

This paper considers the problem of electing an eventual leader in an asynchronous shared memory system. While this problem has received a lot of attention in message- passing systems, very few solutions have been proposed for shared memory systems. As an eventual leader cannot be elected in a pure asynchronous system prone to process crashes, the paper first proposes to enrich the asynchronous system model with an additional assumption. That assumption, denoted AWB, requires that after some time (1) there is a process whose write accesses to some shared variables are timely, and (2) the timers of the other processes are asymptotically well-behaved. The asymptotically well-behaved timer notion is a new notion that generalizes and weakens the traditional notion of timers whose durations are required to monotonically increase when the values they are set to increase. Then, the paper presents two A WB-based algorithms that elect an eventual leader. Both algorithms are independent of the value of t (the maximal number of processes that may crash). The first algorithm enjoys the following noteworthy properties: after some time only the elected leader has to write the shared memory, and all but one shared variables have a bounded domain, be the execution finite or infinite. This algorithm is consequently optimal with respect to the number of processes that have to write the shared memory. The second algorithm enjoys the following property: all the shared variables have a bounded domain. This is obtained at the following additional price: all the processes are required to forever write the shared memory. A theorem is proved which states that this price has to be paid by any algorithm that elects an eventual leader in a bounded shared memory model. This second algorithm is consequently optimal with respect to the number of processes that have to write in such a constrained memory model. In a very interesting way, these algorithms show an inherent tradeoff relating the number of processes that have to write the shared memory and the bounded/unbounded attribute of that memory.