Storage-Efficient Shared Memory Emulation
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We study the design of storage-efficient algorithms for emulating atomic shared memory over an asynchronous, distributed message-passing network. Our first algorithm is an atomic single-writer multi-reader algorithm based on a novel erasure-coding technique, termed multi-version code. Next, we propose an extension of our single-writer algorithm to a multi-writer multi-reader environment. Our second algorithm combines replication and multi-version code, and is suitable in situations where we expect a large number of concurrent writes. Moreover, when the number of concurrent writes is bounded, we propose a simplified variant of the second algorithm that has a simple structure similar to the single-writer algorithm. Let N be the number of servers, and the shared memory variable be of size 1 unit. Our algorithms have the following properties: (i) The algorithms guarantee liveness of the read as long as the number of writes concurrent with the read is smaller than a design parameter ν, and the number of server failures is bounded by a parameter f. Moreover, our algorithms satisfy finite-write termination if we allow readers to retry. (ii) The storage size for the first algorithm, and the steady-state storage size for the second algorithm, are all 1/N-2f/ν unit per server. Moreover, our simplified variant of the second algorithm achieves the worst-case storage cost of 1/N-2f/ν, asymptotically matching a lower bound by Cadambe et al. for N ≫ f, ν≫ 1. (iii) The write and read operations only consist of a small number (2 to 3) of communication rounds. (iv) For all algorithms, the server maintains a simple data structure. A server only needs to store the information associated with the latest value it observes, similar to replication-based algorithms.
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