A Complexity-Based Hierarchy for Multiprocessor Synchronization

For many years, Herlihy's elegant computability based Consensus Hierarchy has been our best explanation of the relative power of various types of multiprocessor synchronization objects when used in deterministic algorithms. However, key to this hierarchy is treating synchronization instructions as distinct objects, an approach that is far from the real-world, where multiprocessor programs apply synchronization instructions to collections of arbitrary memory locations. We were surprised to realize that, when considering instructions applied to memory locations, the computability based hierarchy collapses. This leaves open the question of how to better capture the power of various synchronization instructions. In this paper, we provide an approach to answering this question. We present a hierarchy of synchronization instructions, classified by their space complexity in solving obstruction-free consensus. Our hierarchy provides a classification of combinations of known instructions that seems to fit with our intuition of how useful some are in practice, while questioning the effectiveness of others. We prove an essentially tight characterization of the power of buffered read and write instructions.Interestingly, we show a similar result for multi-location atomic assignments

On the Uncontended Complexity of Anonymous Consensus

Consensus is one of the central distributed abstractions. By enabling a collection of processes to agree on one of the values they propose, consensus can be used to implement any generic replicated service in a consistent and fault-tolerant way. In this paper, we study uncontended complexity of anonymous consensus algorithms, counting the number of memory locations used and the number of memory updates performed in operations that encounter no contention. We assume that contention-free operations on a consensus object perform "fast" reads and writes, and resort to more expensive synchronization primitives, such as CAS, only when contention is detected. We call such concurrent implementations interval-solo-fast and derive one of the first nontrivial tight bounds on space complexity of anonymous interval-solo-fast consensus

Eventual election of multiple leaders for solving consensus in anonymous systems

In classical distributed systems, each process has a unique identity. Today, new distributed systems have emerged where a unique identity is not always possible to be assigned to each process. For example, in many sensor networks a unique identity is not possible to be included in each device due to its small storage capacity, reduced computational power, or the huge number of devices to be identified. In these cases, we have to work with anonymous distributed systems where processes cannot be identified. Consensus cannot be solved in classical and anonymous asynchronous distributed systems where processes can crash. To bypass this impossibility result, failure detectors are added to these systems. It is known that ? is the weakest failure detector class for solving consensus in classical asynchronous systems when amajority of processes never crashes. Although A? was introduced as an anonymous version of ?, to find the weakest failure detector in anonymous systems to solve consensus when amajority of processes never crashes is nowadays an open question. Furthermore, A? has the important drawback that it is not implementable. Very recently, A? has been introduced as a counterpart of ? for anonymous systems. In this paper, we show that the A? failure detector class is strictly weaker than A? (i.e., A? provides less information about process crashes than A?). We also present in this paper the first implementation of A? (hence, we also show that A? is implementable), and, finally, we include the first implementation of consensus in anonymous asynchronous systems augmented with A? and where a majority of processes does not crash

Stretching the capacity of Hardware Transactional Memory in IBM POWER architectures

The hardware transactional memory (HTM) implementations in commercially available processors are significantly hindered by their tight capacity constraints. In practice, this renders current HTMs unsuitable to many real-world workloads of in-memory databases. This paper proposes SI-HTM, which stretches the capacity bounds of the underlying HTM, thus opening HTM to a much broader class of applications. SI-HTM leverages the HTM implementation of the IBM POWER architecture with a software layer to offer a single-version implementation of Snapshot Isolation. When compared to HTM- and software-based concurrency control alternatives, SI-HTM exhibits improved scalability, achieving speedups of up to 300% relatively to HTM on in-memory database benchmarks

The Impact of RDMA on Agreement

Remote Direct Memory Access (RDMA) is becoming widely available in data centers. This technology allows a process to directly read and write the memory of a remote host, with a mechanism to control access permissions. In this paper, we study the fundamental power of these capabilities. We consider the well-known problem of achieving consensus despite failures, and find that RDMA can improve the inherent trade-off in distributed computing between failure resilience and performance. Specifically, we show that RDMA allows algorithms that simultaneously achieve high resilience and high performance, while traditional algorithms had to choose one or another. With Byzantine failures, we give an algorithm that only requires $n \geq 2f_P + 1$ processes (where $f_P$ is the maximum number of faulty processes) and decides in two (network) delays in common executions. With crash failures, we give an algorithm that only requires $n \geq f_P + 1$ processes and also decides in two delays. Both algorithms tolerate a minority of memory failures inherent to RDMA, and they provide safety in asynchronous systems and liveness with standard additional assumptions.Comment: Full version of PODC'19 paper, strengthened broadcast algorith

Notes on Theory of Distributed Systems

Notes for the Yale course CPSC 465/565 Theory of Distributed Systems

The Step Complexity of Multidimensional Approximate Agreement

Approximate agreement allows a set of n processes to obtain outputs that are within a specified distance ? > 0 of one another and within the convex hull of the inputs. When the inputs are real numbers, there is a wait-free shared-memory approximate agreement algorithm [Moran, 1995] whose step complexity is in O(n log(S/?)), where S, the spread of the inputs, is the maximal distance between inputs. There is another wait-free algorithm [Schenk, 1995] that avoids the dependence on n and achieves O(log(M/?)) step complexity where M, the magnitude of the inputs, is the absolute value of the maximal input. This paper considers whether it is possible to obtain an approximate agreement algorithm whose step complexity depends on neither n nor the magnitude of the inputs, which can be much larger than their spread. On the negative side, we prove that ?(min{(log M)/(log log M), (?log n)/(log log n)}) is a lower bound on the step complexity of approximate agreement, even when the inputs are real numbers. On the positive side, we prove that a polylogarithmic dependence on n and S/? can be achieved, by presenting an approximate agreement algorithm with O(log n (log n + log(S/?))) step complexity. Our algorithm works for multidimensional domains. The step complexity can be further restricted to be in O(min{log n (log n + log (S/?)), log(M/?)}) when the inputs are real numbers