Many applications model their data in a general-purpose storage format such as JSON. This data structure is modified by the application as a result of user input. Such modifications are well understood if performed sequentially on a single copy of the data, but if the data is replicated and modified concurrently on multiple devices, it is unclear what the semantics should be. In this paper we present an algorithm and formal semantics for a JSON data structure that automatically resolves concurrent modifications such that no updates are lost, and such that all replicas converge towards the same state (a conflict-free replicated datatype or CRDT). It supports arbitrarily nested list and map types, which can be modified by insertion, deletion and assignment. The algorithm performs all merging client-side and does not depend on ordering guarantees from the network, making it suitable for deployment on mobile devices with poor network connectivity, in peer-to-peer networks, and in messaging systems with end-to-end encryption.

A Commutative Replicated Data Type (CRDT) is one where all concurrent operations commute. The replicas of a CRDT converge automatically, without complex concurrency control. This paper describes Treedoc, a novel CRDT design for cooperative text editing. An essential property is that the identifiers of Treedoc atoms are selected from a dense space. We discuss practical alternatives for implementing the identifier space based on an extended binary tree. We also discuss storage alternatives for data and meta-data, and mechanisms for compacting the tree. In the best case, Treedoc incurs no overhead with respect to a linear text buffer. We validate the results with traces from existing edit histories. 1. Our happened-before and concurrency relations are identical to the formal definition of Lamport [1].

Geo-replicated storage systems are at the core of current Internet services. The designers of the replication protocols used by these systems must choose between either supporting low-latency, eventually-consistent operations, or ensuring strong consistency to ease application correctness. We propose an alternative consistency model, Explicit Consistency, that strengthens eventual consistency with a guarantee to preserve specific invariants defined by the applications. Given these application-specific invariants, a system that supports Explicit Consistency identifies which operations would be unsafe under concurrent execution, and allows programmers to select either violation-avoidance or invariant-repair techniques. We show how to achieve the former, while allowing operations to complete locally in the common case, by relying on a reservation system that moves coordination off the critical path of operation execution. The latter, in turn, allows operations to execute without restriction, and restore invariants by applying a repair operation to the database state. We present the design and evaluation of Indigo, a middleware that provides Explicit Consistency on top of a causally-consistent data store. Indigo guarantees strong application invariants while providing similar latency to an eventually-consistent system in the common case.

Bloom filters provide space-efficient storage of sets at the cost of a probability of false positives on membership queries. The size of the filter must be defined a priori based on the number of elements to store and the desired false positive probability, being impossible to store extra elements without increasing the false positive probability. This leads typically to a conservative assumption regarding maximum set size, possibly by orders of magnitude, and a consequent space waste. This paper proposes Scalable Bloom Filters, a variant of Bloom filters that can adapt dynamically to the number of elements stored, while assuring a maximum false positive probability.