The notion of Timed Registers and its application to Indulgent Synchronization

A new type of shared object, called timed register, is proposed and used to design indulgent timing-based algorithms.A timed register generalizes the notion of an atomic register as follows: if a process invokes two consecutive operations on the same timed register which are a read followed by a write, then the write operation is executed only if it is invoked at most d time units after the read operation, where d is defined as part of the read operation. In this context, a timing-based algorithm is an algorithm whose correctness relies on the existence of a bound $\Delta$ such that any pair of consecutive constrained read and write operations issued by the same process on the same timed register are separated by at most $\Delta$ time units. An indulgent algorithm is an algorithm that always guarantees the safety properties, and ensures the liveness property as soon as the timing assumptions are satisfied. The usefulness of this new type of shared object is demonstrated by presenting simple and elegant indulgent timing-based algorithms that solve the mutual exclusion, $\ell$-exclusion, adaptive renaming, test&set, and consensus problems. Interestingly, timed registers are universal objects in systems with process crashes and transient timing failures (i.e., they allow building any concurrent object with a sequential specification). The paper also suggests connections with schedulers and contention managers

Fast Deterministic Consensus in a Noisy Environment

It is well known that the consensus problem cannot be solved deterministically in an asynchronous environment, but that randomized solutions are possible. We propose a new model, called noisy scheduling, in which an adversarial schedule is perturbed randomly, and show that in this model randomness in the environment can substitute for randomness in the algorithm. In particular, we show that a simplified, deterministic version of Chandra's wait-free shared-memory consensus algorithm (PODC, 1996, pp. 166-175) solves consensus in time at most logarithmic in the number of active processes. The proof of termination is based on showing that a race between independent delayed renewal processes produces a winner quickly. In addition, we show that the protocol finishes in constant time using quantum and priority-based scheduling on a uniprocessor, suggesting that it is robust against the choice of model over a wide range.Comment: Typographical errors fixe

How to Elect a Leader Faster than a Tournament

The problem of electing a leader from among $n$ contenders is one of the fundamental questions in distributed computing. In its simplest formulation, the task is as follows: given $n$ processors, all participants must eventually return a win or lose indication, such that a single contender may win. Despite a considerable amount of work on leader election, the following question is still open: can we elect a leader in an asynchronous fault-prone system faster than just running a $\Theta(\log n)$-time tournament, against a strong adaptive adversary? In this paper, we answer this question in the affirmative, improving on a decades-old upper bound. We introduce two new algorithmic ideas to reduce the time complexity of electing a leader to $O(\log^* n)$, using $O(n^2)$ point-to-point messages. A non-trivial application of our algorithm is a new upper bound for the tight renaming problem, assigning $n$ items to the $n$ participants in expected $O(\log^2 n)$ time and $O(n^2)$ messages. We complement our results with lower bound of $\Omega(n^2)$ messages for solving these two problems, closing the question of their message complexity

Solving the At-Most-Once Problem with Nearly Optimal Effectiveness

We present and analyze a wait-free deterministic algorithm for solving the at-most-once problem: how m shared-memory fail-prone processes perform asynchronously n jobs at most once. Our algorithmic strategy provides for the first time nearly optimal effectiveness, which is a measure that expresses the total number of jobs completed in the worst case. The effectiveness of our algorithm equals n-2m+2. This is up to an additive factor of m close to the known effectiveness upper bound n-m+1 over all possible algorithms and improves on the previously best known deterministic solutions that have effectiveness only n-log m o(n). We also present an iterative version of our algorithm that for any $m = O\left(\sqrt[3+\epsilon]{n/\log n}\right)$ is both effectiveness-optimal and work-optimal, for any constant $\epsilon > 0$. We then employ this algorithm to provide a new algorithmic solution for the Write-All problem which is work optimal for any $m=O\left(\sqrt[3+\epsilon]{n/\log n}\right)$.Comment: Updated Version. A Brief Announcement was published in PODC 2011. An Extended Abstract was published in the proceeding of ICDCN 2012. A full version was published in Theoretical Computer Science, Volume 496, 22 July 2013, Pages 69 - 8

Randomized versus Deterministic Implementations of Concurrent Data Structures

One of the key trends in computing over the past two decades has been increased distribution, both at the processor level, where multi-core architectures are now the norm, and at the system level, where many key services are currently distributed overmultiple machines. Thus, understanding the power and limitations of computing in a concurrent, distributed setting is one of the major challenges in Computer Science. In this thesis, we analyze the complexity of implementing concurrent data structures in asynchronous shared memory systems. We focus on the complexity of a classic distributed coordination task called renaming, in which a set of processes need to pick distinct names from a small set of identifiers. We present the first tight bounds for the time complexity of this problem, both for deterministic and randomized implementations, solving a long-standing open problem in the field. For deterministic algorithms, we prove a tight linear lower bound; for randomized solutions, we provide logarithmic upper and lower bounds on time complexity. Together, these results show an exponential separation between deterministic and randomized renaming solutions. Importantly, the lower bounds extend to implementations of practical shared-memory data structures, such as queues, stacks, and counters. From a technical perspective, this thesis highlights new connections between the distributed renaming problem and other fundamental objects, such as sorting networks, mutual exclusion, and counters. In particular, we show that sorting networks can be used to obtain optimal randomized solutions to renaming, and that, in turn, the existence of these solutions implies a linear lower bound on the complexity of the problem. In sum, the results in this thesis suggest that deterministic implementations of shared-memory data structures do not scale well in terms of worst-case time complexity. On the positive side, we emphasize randomization as a natural alternative, which can circumvent the deterministic lower bounds with high probability. Thus, a promising direction for future work is to extend our randomized renaming techniques to obtain efficient implementations of concurrent data structures

Notes on Theory of Distributed Systems

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

The Computational Power of Distributed Shared-Memory Models with Bounded-Size Registers

The celebrated Asynchronous Computability Theorem of Herlihy and Shavit (STOC 1993 and STOC 1994) provided a topological characterization of the tasks that are solvable in a distributed system where processes are communicating by writing and reading shared registers, and where any number of processes can fail by crashing. However, this characterization assumes the use of full-information protocols, that is, protocols in which each time any of the processes writes in the shared memory, it communicates everything it learned since the beginning of the execution. Thus, the characterization implicitly assumes that each register in the shared memory is of unbounded size. Whether unbounded size registers are unavoidable for the model of computation to be universal is the central question studied in this paper. Specifically, is any task that is solvable using unbounded registers solvable using registers of bounded size? More generally, when at most $t$ processes can crash, is the model with bounded size registers universal? These are the questions answered in this paper

Randomized loose renaming in O(log log n) time

International audienceRenaming is a classic distributed coordination task in which a set of processes must pick distinct identifiers from a small namespace. In this paper, we consider the time complexity of this problem when the namespace is linear in the number of participants, a variant known as loose renaming. We give a non-adaptive algorithm with $O( \log \log n )$ (individual) step complexity, where $n$ is a known upper bound on contention, and an adaptive algorithm with step complexity $O( (\log \log k)^2 )$, where $k$ is the actual contention in the execution. We also present a variant of the adaptive algorithm which requires $O( k \log \log k )$ \emph{total} process steps. All upper bounds hold with high probability against a strong adaptive adversary. We complement the algorithms with an $\Omega( \log \log n )$ expected time lower bound on the complexity of randomized renaming using test-and-set operations and linear space. The result is based on a new coupling technique, and is the first to apply to non-adaptive randomized renaming. Since our algorithms use $O(n)$ test-and-set objects, our results provide matching bounds on the cost of loose renaming in this setting

Recoverable, Abortable, and Adaptive Mutual Exclusion with Sublogarithmic RMR Complexity

We present the first recoverable mutual exclusion (RME) algorithm that is simultaneously abortable, adaptive to point contention, and with sublogarithmic RMR complexity. Our algorithm has O(min(K,log_W N)) RMR passage complexity and O(F + min(K,log_W N)) RMR super-passage complexity, where K is the number of concurrent processes (point contention), W is the size (in bits) of registers, and F is the number of crashes in a super-passage. Under the standard assumption that W = ?(log N), these bounds translate to worst-case O((log N)/(log log N)) passage complexity and O(F + (log N)/(log log N)) super-passage complexity. Our key building blocks are: - A D-process abortable RME algorithm, for D ? W, with O(1) passage complexity and O(1+F) super-passage complexity. We obtain this algorithm by using the Fetch-And-Add (FAA) primitive, unlike prior work on RME that uses Fetch-And-Store (FAS/SWAP). - A generic transformation that transforms any abortable RME algorithm with passage complexity of B < W, into an abortable RME lock with passage complexity of O(min(K,B))