Consistent, Order-Preserving Data Management in Distributed Storage Systems

In this paper we consider the problem of maintaining a mapping of data objects to memory modulesso that the mapping is order preserving, i.e. objects closely together in the sorted set of current objectsare also closely together in the mapping. Keeping close objects closely together is important for manyapplications such as efficiently executing programs using a large amount of space or complex searchqueries such as semi-group range queries. Our main result assumes a static set of memory modules ofuniform capacity, but we also show how to extend this to a dynamic set of memory modules of non-uniform capacity in a decentralized environment.We assume that insert and delete requests of objects are continuously injected into the system, andthe injection is under adversarial control. Data objects are of uniform size and every module can send orreceive at most one object in each unit of time. We prove asymptotically tight upper and lower bounds forthe maximum rate at which the adversary can inject update requests into the modules so that an orderedplacement can be preserved without exceeding the capacity of a module at any time. Specifically, weshow that in a (1− ǫ)-utilized system (i.e. the available space is used up to an ǫ fraction) the maximuminjection rate that can be sustained is Θ(ǫ). While this does not seem to be particularly surprising, it isactually hard to prove in a rigorous way.Besides having interesting consequences for distributed storage and information systems, we alsofeel that our approach offers interesting future problems for theoretical research.