Data sketches are approximate succinct summaries of long data streams. They are widely used for processing massive amounts of data and answering statistical queries about it. Existing libraries producing sketches are very fast, but do not allow parallelism for creating sketches using multiple threads or querying them while they are being built. We present a generic approach to parallelising data sketches efficiently and allowing them to be queried in real time, while bounding the error that such parallelism introduces. Utilising relaxed semantics and the notion of strong linearisability we prove our algorithm's correctness and analyse the error it induces in two specific sketches. Our implementation achieves high scalability while keeping the error small. We have contributed one of our concurrent sketches to the open-source data sketches library.
We propose DSON, a space efficient δ-based CRDT approach for distributed JSON document stores, enabling high availability at a global scale, while providing
strong
eventual consistency guarantees. We define the semantics of our CRDT based approach formally, and prove its correctness and convergence. Previous approaches optimize for collaborative document editing and store metadata proportional to the number of updates to a document, which is not acceptable for long lived document management. The metadata stored with our approach is bounded by
O
(
k
2
D
+
n
log
n
), where
n
is the number of replicas,
D
is the number of document elements, and
k
≤
n
is the number of concurrent document updates. We also implement our approach[37] and demonstrate its space efficiency empirically. Experimental analysis shows that the metadata stored is typically significantly less than the worst case. This provides the basis for robust highly available distributed document stores with well defined semantics and safety guarantees, relieving application developers from the burden of conflict resolution.
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