Distributed Sparse Signal Recovery For Sensor Networks

We propose a distributed algorithm for sparse signal recovery in sensor networks based on Iterative Hard Thresholding (IHT). Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their collective measurements at a minimal communication cost and with low computational complexity. A naive distributed implementation of IHT would require global communication of every agent's full state in each iteration. We find that we can dramatically reduce this communication cost by leveraging solutions to the distributed top-K problem in the database literature. Evaluations show that our algorithm requires up to three orders of magnitude less total bandwidth than the best-known distributed basis pursuit method

Intermediate Value Linearizability: A Quantitative Correctness Criterion

Big data processing systems often employ batched updates and data sketches to estimate certain properties of large data. For example, a CountMin sketch approximates the frequencies at which elements occur in a data stream, and a batched counter counts events in batches. This paper focuses on the correctness of concurrent implementations of such objects. Specifically, we consider quantitative objects, whose return values are from a totally ordered domain, with an emphasis on $(e,d)$-bounded objects that estimate a quantity with an error of at most $e$ with probability at least $1 - d$. The de facto correctness criterion for concurrent objects is linearizability. Under linearizability, when a read overlaps an update, it must return the object's value either before the update or after it. Consider, for example, a single batched increment operation that counts three new events, bumping a batched counter's value from $7$ to $10$. In a linearizable implementation of the counter, an overlapping read must return one of these. We observe, however, that in typical use cases, any intermediate value would also be acceptable. To capture this degree of freedom, we propose Intermediate Value Linearizability (IVL), a new correctness criterion that relaxes linearizability to allow returning intermediate values, for instance $8$ in the example above. Roughly speaking, IVL allows reads to return any value that is bounded between two return values that are legal under linearizability. A key feature of IVL is that concurrent IVL implementations of $(e,d)$-bounded objects remain $(e,d)$-bounded. To illustrate the power of this result, we give a straightforward and efficient concurrent implementation of an $(e, d)$-bounded CountMin sketch, which is IVL (albeit not linearizable). Finally, we show that IVL allows for inherently cheaper implementations than linearizable ones

Dynamic Atomic Snapshots

Snapshots are useful tools for monitoring big distributed and parallel systems. In this paper, we adapt the well-known atomic snapshot abstraction to dynamic models with an unbounded number of participating processes. Our dynamic snapshot specification extends the API to allow changing the set of processes whose values should be returned from a scan operation. We introduce the ephemeral memory model, which consists of a dynamically changing set of nodes; when a node is removed, its memory can be immediately reclaimed. In this model, we present an algorithm for wait-free dynamic atomic snapshots

On Payment Channels in Asynchronous Money Transfer Systems

Money transfer is an abstraction that realizes the core of cryptocurrencies. It has been shown that, contrary to common belief, money transfer in the presence of Byzantine faults can be implemented in asynchronous networks and does not require consensus. Nonetheless, existing implementations of money transfer still require a quadratic message complexity per payment, making attempts to scale hard. In common blockchains, such as Bitcoin and Ethereum, this cost is mitigated by payment channels implemented as a second layer on top of the blockchain allowing to make many off-chain payments between two users who share a channel. Such channels require only on-chain transactions for channel opening and closing, while the intermediate payments are done off-chain with constant message complexity. But payment channels in-use today require synchrony; therefore, they are inadequate for asynchronous money transfer systems. In this paper, we provide a series of possibility and impossibility results for payment channels in asynchronous money transfer systems. We first prove a quadratic lower bound on the message complexity of on-chain transfers. Then, we explore two types of payment channels, unidirectional and bidirectional. We define them as shared memory abstractions and prove that in certain cases they can be implemented as a second layer on top of an asynchronous money transfer system whereas in other cases it is impossible

Tame the Wild with Byzantine Linearizability: Reliable Broadcast, Snapshots, and Asset Transfer

We formalize Byzantine linearizability, a correctness condition that specifies whether a concurrent object with a sequential specification is resilient against Byzantine failures. Using this definition, we systematically study Byzantine-tolerant emulations of various objects from registers. We focus on three useful objects- reliable broadcast, atomic snapshot, and asset transfer. We prove that there exist n-process f-resilient Byzantine linearizable implementations of such objects from registers if and only if f < n/2