Abstract-Erasure codes are increasingly being studied in the context of implementing atomic memory objects in large scale asynchronous distributed storage systems. When compared with the traditional replication based schemes, erasure codes have the potential of significantly lowering storage and communication costs while simultaneously guaranteeing the desired resiliency levels. In this work, we propose the Storage-Optimized DataAtomic (SODA) algorithm for implementing atomic memory objects in the multi-writer multi-reader setting. SODA uses Maximum Distance Separable (MDS) codes, and is specifically designed to optimize the total storage cost for a given faulttolerance requirement. For tolerating f server crashes in an nserver system, SODA uses an [n, k] MDS code with k = n−f , and incurs a total storage cost of We also present a modification of SODA, called SODAerr, to handle the case where some of the servers can return erroneous coded elements during a read operation. Specifically, in order to tolerate f server failures and e error-prone coded elements, the SODAerr algorithm uses an [n, k] MDS code such that k = n − 2e − f . SODAerr also guarantees liveness and atomicity, while maintaining an optimized total storage cost of n n−f −2e .

Emulating atomic read/write shared objects in a message-passing system is a fundamental problem in distributed computing. Considering that network communication is the most expensive resource, efficiency is measured first of all in terms of the communication needed to implement read and write operations. It is well known that two communication round-trip phases involving in total four message exchanges are sufficient to implemented atomic operations. It is also known that under certain constraints on the number of readers with respect to the numbers of replica servers and failures it is possible to implement single-writer atomic objects such that each operation involves one round-trip phase, or two message exchanges.In this work we present a comprehensive treatment of the question on when and how it is possible to implement atomic memory where read and write operations complete in three message exchanges, i.e., we aim for One and half Round Atomic Memory, hence the name Oh-RAM! We present algorithms that allow operations to complete in three communication exchanges without imposing any constraints on the number of readers and writers. Specifically, we present an atomic memory implementation for the single-writer/multiple-reader (SWMR) setting, where reads complete in three communication exchanges and writes complete in two exchanges. We pose the question of whether it is possible to implement multiple-writer/multiple-reader (MWMR) memory where operations complete in at most three communication exchanges. We answer this question in the negative by showing that an atomic memory implementation is impossible if both read and write operations take three communication exchanges. Motivated by this impossibility result, we provide a MWMR atomic memory implementation where reads involve three and writes involve four communication exchanges. In light of our impossibility result these algorithms are optimal in terms of the number of communication exchanges. We rigorously reason about the correctness of the algorithms.

Providing efficient emulations of atomic read/write objects in asynchronous, crash-prone, message-passing systems is an important problem in distributed computing. Communication latency is a factor that typically dominates the performance of message-passing systems, consequently the efficiency of algorithms implementing atomic objects is measured in terms of the number of communication exchanges involved in each read and write operation. The seminal result of Attiya, Bar-Noy, and Dolev established that two pairs of communication exchanges, or equivalently two round-trip communications, are sufficient. Subsequent research examined the possibility of implementations that involve less than four exchanges. The work of Dutta et al. showed that for single-writer/multiple-reader (SWMR) settings two exchanges are sufficient, provided that the number of readers is severely constrained with respect to the number of object replicas in the system and the number of replica failures, and also showed that no twoexchange implementations of multiple-writer/multiple-reader (MWMR) objects are possible. Later research focused on providing implementations that remove the constraint on the number of readers, while having read and write operations that use variable number of communication exchanges, specifically two, three, or four exchanges.This work presents two advances in the state-of-the-art in this area. Specifically, for SWMR and MWMR systems algorithms are given in which read operations take two or three exchanges. This improves on prior works where read operations took either (a) three exchanges, or (b) two or four exchanges. The number of readers in the new algorithms is unconstrained, and write operations take the same number of exchanges as in prior work (two for SWMR and four for MWMR settings). The correctness of algorithms is rigorously argued. The paper presents an empirical study using the NS3 simulator that compares the performance of relevant algorithms, demonstrates the practicality of the new algorithms, and identifies settings in which their performance is clearly superior.

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