Coded Emulation of Shared Atomic Memory for Message Passing Architectures

This paper considers the communication and storage costs of emulating atomic (linearizable) read/write shared memory in distributed messagepassing systems. We analyze the costs of previously-proposed algorithms by Attiya, Bar-Noy, and Dolev (the ABD algorithm) and by Fan and Lynch (the LDR algorithm), and develop new coding-based algorithms that significantly reduce these costs. The paper contains three main contributions: (1) We present a new shared-memory algorithm that we call CAS, for Coded Atomic Storage. This algorithm uses erasure coding methods. (2) In a storage system withN servers that is resilient to f server failures, we show that the communication costs for the ABD and LDR algorithms, measured in terms of number of object values, are both at least f + 1, whereas the communication cost for CAS is N N−2f . (3) We also explicitly quantify the storage costs of the ABD, LDR, and CAS algorithms. The storage cost of the ABD algorithm, measured in terms of number of object values, is N, whereas the storage costs of the LDR and CAS algorithms are both unbounded. We present a modification of the CAS algorithm based on the idea of garbage collection. The modified version of CAS has a storage cost of (δ + 1) N N−2f , where δ in an upper bound on the number of operations that are concurrent with a read operation. Thus, if δ is sufficiently small, the storage cost of CAS is lower than those of both the ABD and LDR algorithms.