[论文解读] Lower Bounds and Algorithm for Partially Replicated Causally Consistent Shared Memory.

Zhuolun Xiang, Nitin H. Vaidya|arXiv (Cornell University)|Mar 15, 2017

Distributed systems and fault tolerance被引用 3

一句话总结

本文通过引入基于共享图的时戳机制，建立了部分复制的分布式共享内存系统中因果一致性的必要且充分条件。它提出了一种符合该条件的高效算法，并推导出时戳大小的紧致下界，证明了在关键情形下的最优性。

ABSTRACT

The focus of this paper is on causal consistency in a {\em partially replicated} distributed shared memory (DSM) system that provides the abstraction of shared read/write registers. Maintaining causal consistency in distributed shared memory systems has received significant attention in the past, mostly on {\em full replication} wherein each replica stores a copy of all the registers in the shared memory. To ensure causal consistency, all causally preceding updates must be performed before an update is performed at any given replica. Therefore, some mechanism for tracking causal dependencies is required, such as vector timestamps with the number of vector elements being equal to the number of replicas in the context of full replication. In this paper, we investigate causal consistency in {\em partially replicated systems}, wherein each replica may store only a subset of the shared registers. Building on the past work, this paper makes three key contributions: 1. We present a necessary condition on the metadata (which we refer as a {\em timestamp}) that must be maintained by each replica to be able to track causality accurately. The necessary condition identifies a set of directed edges in a {\em share graph} that a replica's timestamp must keep track of. 2. We present an algorithm for achieving causal consistency using a timestamp that matches the above necessary condition, thus showing that the condition is necessary and sufficient. 3. We define a measurement of timestamp space size and present a lower bound (in bits) on the size of the timestamps. The lower bound matches our algorithm in several special cases.

研究动机与目标

• 为解决在仅存储部分共享寄存器子集的副本的、部分复制的分布式共享内存系统中保持因果一致性的挑战。
• 识别出准确追踪副本间因果依赖关系所需的最小元数据（时戳）要求。
• 设计一种算法，使用满足推导出的必要条件的时戳，实现因果一致性。
• 建立时戳空间大小的理论下界，确保在关键系统配置下的效率与最优性。

提出的方法

• 引入共享图以建模更新之间的因果关系，其中节点代表副本，有向边代表因果依赖。
• 将时戳定义为必须追踪共享图中特定有向边的数据结构，以保持因果顺序。
• 提出一种使用共享图感知时戳的算法，以在读写操作期间强制实现因果一致性。
• 通过分析必须表示的不同因果依赖模式的数量，推导出时戳大小（以位为单位）的下界。
• 证明所提算法的时戳大小在特殊情形下与推导出的下界一致，从而证明其最优性。
• 采用适配于部分复制的向量时戳技术，其中元素数量不依赖于总副本数，而是依赖于因果关系。

实验结果

研究问题

• RQ1 在部分复制的共享内存系统中，正确追踪因果依赖关系所需的最小元数据结构是什么？
• RQ2 能否设计一种算法，仅使用由条件识别出的必要元数据，实现因果一致性？
• RQ3 为确保此类系统中的因果一致性，时戳所需的理论最小大小（以位为单位）是多少？
• RQ4 所提算法是否在系统配置的有意义特殊情形下达到该下界？

主要发现

• 在部分复制系统中实现因果一致性的必要条件是：每个副本的时戳必须追踪共享图中的特定一组有向边。
• 提出了一种满足必要条件的算法，从而确保因果一致性，证明该条件也是充分的。
• 本文建立了时戳大小的下界（以位为单位），量化了实现因果一致性所需的最小元数据开销。
• 该下界在多个重要特殊情形下与所提算法使用的时戳大小一致，表明该算法在这些配置下是最优的。
• 共享图抽象能够精确建模因果依赖关系，而无需全量复制或全局协调。
• 结果表明，只要使用正确的时戳结构，部分复制系统中的因果一致性可在极小元数据开销下实现。