# Lower Bounds and Algorithm for Partially Replicated Causally Consistent Shared Memory

Distributed shared memory systems maintain multiple replicas of the shared memory locations. Maintaining causal consistency in such systems has received significant attention in the past. However, much of the previous literature focuses on full replication wherein each replica stores a copy of all the locations in the shared memory. In this paper, we investigate causal consistency in partially replicated systems, wherein each replica may store only a subset of the shared data. To achieve causal consistency, it is necessary to ensure that, before an update is performed at any given replica, all causally preceding updates must also be performed. Achieving this goal requires some mechanism to track causal dependencies. In the context of full replication, this goal is often achieved using vector timestamps, with the number of vector elements being equal to the number of replicas. Building on the past work, this paper makes three key contributions: 1. We develop lower bounds on the size of the timestamps that must be maintained in order to achieve causal consistency in partially replicated systems. The size of the timestamps is a function of the manner in which the replicas share data, and the set of replicas accessed by each client. 2. We present an algorithm to achieve causal consistency in partially replicated systems using simple vector timestamps. 3. We present some optimizations to improve the overhead of the timestamps required with partial replication.

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