Emulating a shared register can mask the intricacies of designing algorithms for asynchronous message-passing systems subject to crash failures, since it allows them to run algorithms designed for the simpler shared-memory model. Typically such emulations replicate the value of the register in multiple servers and require readers and writers to communicate with a majority of servers. The success of this approach for static systems, where the set of nodes (readers, writers, and servers) is fixed, has motivated several similar emulations for dynamic systems, where nodes may enter and leave. However, existing emulations need to assume that the system eventually stops changing for a long enough period or that the system size is bounded. This paper presents the first emulation of a register supporting any number of readers and writers in a crash-prone system that can withstand nodes continually entering and leaving and imposes no upper bound on the system size. The algorithm works as long as the number of nodes entering and leaving during a fixed time interval is at most a constant fraction of the system size at the beginning of the interval, and as long as the number of crashed nodes in the system is at most a constant fraction of the current system size. The paper includes a lower bound on the fraction of correct nodes that is strictly larger than the fraction sufficient to solve the problem in the static case.

A key challenge for wireless networks in which nodes can move is for each node to keep track of its dynamically changing set of nearby nodes (neighbors). We present a solution for nodes to maintain neighbor knowledge where nodes communicate via wireless broadcast and are restricted to move on a two-dimensional road network. A road network is a collection of one-dimensional lines that may intersect each other. For nodes to exchange neighbor information, we construct a deterministic collision-free broadcast schedule which utilizes time division multiplexing and geographical segmentation. Under a certain node density requirement and assuming initial neighbor knowledge, our broadcast schedule tolerates node movement on the road network while providing deterministic guarantees in maintaining neighbor knowledge. We also provide a lower bound on the speed of a message propagation given our broadcast schedule. In addition, we consider grouping nodes into clusters and show that, under certain conditions, neighbor knowledge is maintained when two different clusters move close to each other. Finally, we address the issue of obtaining initial neighbor knowledge.