Asynchronous Shared Memory System Research Articles

FEAST

We present a lock-free algorithm for concurrent manipulation of a binary search tree (BST) in an asynchronous shared memory system that supports search, insert, and delete operations. In addition to read and write instructions, our algorithm uses (single-word) compare-and-swap (CAS) and bit-test-and-set (BTS) read-modify-write (RMW) instructions, both of which are commonly supported by many modern processors including Intel 64 and AMD64. In contrast to most of the existing concurrent algorithms for a binary search tree, our algorithm is edge-based rather than node-based. When compared to other concurrent algorithms for a binary search tree, modify (insert and delete) operations in our algorithm (a) work on a smaller section of the tree, (b) execute fewer RMW instructions, or (c) use fewer dynamically allocated objects. In our experiments, our lock-free algorithm significantly outperformed all other algorithms for a concurrent binary search tree especially when the contention was high. We also describe modifications to our basic lock-free algorithm so that the amortized complexity of any operation in the modified algorithm can be bounded by the sum of the tree height and the point contention to within a constant factor while preserving the other desirable features of our algorithm.

Non-blocking Patricia tries with replace operations

This paper presents a non-blocking Patricia trie implementation for an asynchronous shared-memory system using Compare&Swap. The trie is a linearizable implementation of a set and supports three update operations: insert adds an element to the trie, delete removes an element from the trie and replace replaces one element by another. The replace operation is interesting because it changes two different locations of a trie. We design a mechanism that allows the two changes of a replace operation to appear to be executed atomically. If all update operations modify different parts of the trie, they run completely concurrently. The implementation also supports a wait-free find operation, which only reads shared memory and never changes the data structure. Our implementation and its correctness proof are modular and can be adapted for other data structures. Empirically, we compare our algorithms to some existing tree-based set implementations and our results show that our trie performs consistently well in different scenarios.

Improving efficacy of internal binary search trees using local recovery

Binary Search Tree (BST) is an important data structure for managing ordered data. Many algorithms---blocking as well as non-blocking---have been proposed for concurrent manipulation of a binary search tree in an asynchronous shared memory system that supports search, insert and delete operations based on both external and internal representations of a search tree. An important step in executing an operation on a tree is to traverse the tree from top-to-down in order to locate the operation's window. A process may need to perform this traversal several times to handle any failures occurring due to other processes performing conflicting actions on the tree. Most concurrent algorithms that have proposed so far use a naïve approach and simply restart the traversal from the root of the tree. In this work, we present a new approach to recover from such failures more efficiently in a concurrent binary search tree based on internal representation using local recovery by restarting the traversal from the "middle" of the tree in order to locate an operation's window. Our approach is sufficiently general in the sense that it can be applied to a variety of concurrent binary search trees based on both blocking and non-blocking approaches. Using experimental evaluation, we demonstrate that our local recovery approach can yield significant speed-ups of up to 69% for many concurrent algorithms.

CASTLE: fast concurrent internal binary search tree using edge-based locking

We present a new lock-based algorithm for concurrent manipulation of a binary search tree in an asynchronous shared memory system that supports search, insert and delete operations. Some of the desirable characteristics of our algorithm are: (i) a search operation uses only read and write instructions, (ii) an insert operation does not acquire any locks, and (iii) a delete operation only needs to lock up to four edges in the absence of contention. Our algorithm is based on an internal representation of a search tree and it operates at edge-level (locks edges) rather than at node-level (locks nodes); this minimizes the contention window of a write operation and improves the system throughput. Our experiments indicate that our lock-based algorithm outperforms existing algorithms for a concurrent binary search tree for medium-sized and larger trees, achieving up to 59% higher throughput than the next best algorithm.

Fast concurrent lock-free binary search trees

We present a new lock-free algorithm for concurrent manipulation of a binary search tree in an asynchronous shared memory system that supports search, insert and delete operations. In addition to read and write instructions, our algorithm uses (single-word) compare-and-swap (CAS) and bit-test-and-set (SETB) atomic instructions, both of which are commonly supported by many modern processors including Intel~64 and AMD64. In contrast to existing lock-free algorithms for a binary search tree, our algorithm is based on marking edges rather than nodes. As a result, when compared to other lock-free algorithms, modify (insert and delete) operations in our algorithm work on a smaller portion of the tree, thereby reducing conflicts, and execute fewer atomic instructions (one for insert and three for delete). Our experiments indicate that our lock-free algorithm significantly outperforms all other algorithms for a concurrent binary search tree in many cases, especially when contention is high, by as much as 100%.

The Complexity of Early Deciding Set Agreement

In the k-set agreement problem, each processor starts with a private input value and eventually decides on an output value. At most k distinct output values may be chosen, and every processor's output value must be one of the proposed values. We consider a synchronous message passing system, and we prove a tight bound of $\lfloor f/k\rfloor+2$ rounds of communication for all processors to decide in every run in which at most f processors fail. The lower bound proof proceeds through a simulation of a synchronous solution to k-set agreement in message passing, in an asynchronous shared memory system in which $k-1$ processors may fail, and which was proven to be impossible using topological approaches. In contrast to past complexity results on set agreement, our lower bound proof is purely algorithmic. It does not use any direct topological argument but uses instead the impossibility of asynchronous set agreement to encapsulate the needed topology. We thus derive an adaptive complexity lower bound for a message passing system from a static impossibility in a shared memory system.

Tight bounds for asynchronous randomized consensus

A distributed consensus algorithm allows n processes to reach a common decision value starting from individual inputs. Wait-free consensus, in which a process always terminates within a finite number of its own steps, is impossible in an asynchronous shared-memory system. However, consensus becomes solvable using randomization when a process only has to terminate with probability 1. Randomized consensus algorithms are typically evaluated by their total step complexity , which is the expected total number of steps taken by all processes. This article proves that the total step complexity of randomized consensus is Θ( n 2 ) in an asynchronous shared memory system using multi-writer multi-reader registers. This result is achieved by improving both the lower and the upper bounds for this problem. In addition to improving upon the best previously known result by a factor of log 2 n , the lower bound features a greatly streamlined proof. Both goals are achieved through restricting attention to a set of layered executions and using an isoperimetric inequality for analyzing their behavior. The matching algorithm decreases the expected total step complexity by a log n factor, by leveraging the multi-writing capability of the shared registers. Its correctness proof is facilitated by viewing each execution of the algorithm as a stochastic process and applying Kolmogorov's inequality.

A Timing Assumption and Two t-Resilient Protocols for Implementing an Eventual Leader Service in Asynchronous Shared Memory Systems

This paper considers the problem of electing an eventual leader in an asynchronous shared memory system. While this problem has received a lot of attention in message-passing systems, very few solutions have been proposed for shared memory systems. As an eventual leader cannot be elected in a pure asynchronous system prone to process crashes, the paper first proposes to enrich the asynchronous system model with an additional assumption. That assumption (denoted AWB) is particularly weak. It is made up of two complementary parts. More precisely, it requires that, after some time, (1) there is a process whose write accesses to some shared variables be timely, and (2) the timers of (t−f) other processes be asymptotically well-behaved (t denotes the maximal number of processes that may crash, and f the actual number of process crashes in a run). The asymptotically well-behaved timer notion is a new notion that generalizes and weakens the traditional notion of timers whose durations are required to monotonically increase when the values they are set to increase (a timer works incorrectly when it expires at arbitrary times, i.e., independently of the value it has been set to).The paper then focuses on the design of t-resilient AWB-based eventual leader protocols. “t-resilient” means that each protocol can cope with up to t process crashes (taking t=n−1 provides wait-free protocols, i.e., protocols that can cope with any number of process failures). Two protocols are presented. The first enjoys the following noteworthy properties: after some time only the elected leader has to write the shared memory, and all but one shared variables have a bounded domain, be the execution finite or infinite. This protocol is consequently optimal with respect to the number of processes that have to write the shared memory. The second protocol guarantees that all the shared variables have a bounded domain. This is obtained at the following additional price: t+1 processes are required to forever write the shared memory. A theorem is proved which states that this price has to be paid by any protocol that elects an eventual leader in a bounded shared memory model. This second protocol is consequently optimal with respect to the number of processes that have to write in such a constrained memory model. In a very interesting way, these protocols show an inherent tradeoff relating the number of processes that have to write the shared memory and the bounded/unbounded attribute of that memory.

Relationships between broadcast and shared memory in reliable anonymous distributed systems

We study the power of reliable anonymous distributed systems, where processes do not fail, do not have identifiers, and run identical programmes. We are interested specifically in the relative powers of systems with different communication mechanisms: anonymous broadcast, read-write registers, or read-write registers plus additional shared-memory objects. We show that a system with anonymous broadcast can simulate a system of shared-memory objects if and only if the objects satisfy a property we call idemdicence this result holds regardless of whether either system is synchronous or asynchronous. Conversely, the key to simulating anonymous broadcast in anonymous shared memory is the ability to count: broadcast can be simulated by an asynchronous shared-memory system that uses only counters, but read-write registers by themselves are not enough. We further examine the relative power of different types and sizes of bounded counters and conclude with a non-robustness result.

Bounded Concurrent Time-Stamping

We introduce concurrent time-stamping, a paradigm that allows processes to temporally order concurrent events in an asynchronous shared-memory system. Concurrent time-stamp systems are powerful tools for concurrency control, serving as the basis for solutions to coordination problems such as mutual exclusion, $\ell$-exclusion, randomized consensus, and multiwriter multireader atomic registers. Unfortunately, all previously known methods for implementing concurrent time-stamp systems have been theoretically unsatisfying since they require unbounded-size time-stamps---in other words, unbounded-size memory. This work presents the first bounded implementation of a concurrent time-stamp system, providing a modular unbounded-to-bounded transformation of the simple unbounded solutions to problems such as those mentioned above. It allows solutions to two formerly open problems, the bounded-probabilistic-consensus problem of Abrahamson and the fifo-$\ell$-exclusion problem of Fischer, Lynch, Burns and Borodin, and a more efficient construction of multireader multiwriter atomic registers.