Time Bounds for Strong and Hybrid Consistency for Arbitrary Abstract Data Types

We compare the costs of three well-known consistency guarantees (sequential consistency, linearizability, and hybrid consistency) for shared memory objects of arbitrary data types, generalizing previous work on specific types. We evaluate the impact of the desired consistency guarantee, the amount of synchrony among the users of the objects, and algebraic properties of a type on the worst-case time complexity of operations of the type. These algebraic properties are sufficient for proving many lower bounds and some upper bounds (even 0, meaning only local computation is required) on the worstcase times. Under certain reasonable assumptions, sequential consistency and linearizability are equally costly in perfectly synchronized systems, linearizable operations are more expensive in approximately synchronized systems than in perfectly synchronized systems, sequentially consistent operations are cheaper than linearizable operations in approximately synchronized systems, and hybrid consistency is not necessarily cheaper than sequential consistency or linearizability.