  Motivated by recent distributed systems technology, Aguilera et al.
introduced a hybrid model of distributed computing, called message-and-memory
model or m&m model for short [1]. In this model, processes can communicate by
message passing and also by accessing some shared memory (e.g., through some
RDMA connections). We first consider the basic problem of implementing an
atomic single-writer multi-reader (SWMR) register shared by all the processes
in m&m systems. Specifically, we give an algorithm that implements such a
register in m&m systems and show that it is optimal in the number of process
crashes that it can tolerate. This generalizes the well-known implementation of
an atomic SWMR register in a pure message-passing system [5]. We then combine
our register implementation for m&m systems with the well-known randomized
consensus algorithm of Aspnes and Herlihy [4], and obtain a randomized
consensus algorithm for m&m systems that is also optimal in the number of
process crashes that it can tolerate. Finally, we determine the minimum number
of RDMA connections that is sufficient to implement a SWMR register, or solve
randomized consensus, in an m&m system with t process crashes, for any given t.

Distributed, Parallel, and Cluster Computing;Data Structures and Algorithms