Concurrent Binary Search Tree Research Articles

Proving highly-concurrent traversals correct

Modern highly-concurrent search data structures, such as search trees, obtain multi-core scalability and performance by having operations traverse the data structure without any synchronization. As a result, however, these algorithms are notoriously difficult to prove linearizable, which requires identifying a point in time in which the traversal's result is correct. The problem is that traversing the data structure as it undergoes modifications leads to complex behaviors, necessitating intricate reasoning about all interleavings of reads by traversals and writes mutating the data structure. In this paper, we present a general proof technique for proving unsynchronized traversals correct in a significantly simpler manner, compared to typical concurrent reasoning and prior proof techniques. Our framework relies only on sequential properties of traversals and on a conceptually simple and widely-applicable condition about the ways an algorithm's writes mutate the data structure. Establishing that a target data structure satisfies our condition requires only simple concurrent reasoning, without considering interactions of writes and reads. This reasoning can be further simplified by using our framework. To demonstrate our technique, we apply it to prove several interesting and challenging concurrent binary search trees: the logical-ordering AVL tree, the Citrus tree, and the full contention-friendly tree. Both the logical-ordering tree and the full contention-friendly tree are beyond the reach of previous approaches targeted at simplifying linearizability proofs.

A Scalable and Energy-Efficient Concurrent Binary Search Tree With Fatnodes

In the recent past, devising algorithms for concurrent data structures has been driven by the need for scalability. Further, there is an increased traction across the industry towards power efficient concurrent data structure designs. In this context, we introduce a scalable and energy-efficient concurrent binary search tree with fatnodes (namely, FatCBST) , and present algorithms to perform basic operations on it. Unlike a single node with one value, a fatnode consists of a set of values. FatCBST minimizes structural changes while performing update operations on the tree. In addition, fatnodes help to exploit the spatial locality in the cache hierarchy and also reduce the height of the tree. FatCBST allows multiple threads to perform update operations on an existing fatnode simultaneously. Experimental results show that for low contention workloads as well as large set sizes, FatCBST scales well and also provides high performance-per-watt values as compared to the state-of-the-art implementations. For high contention workloads with small set sizes, FatCBST suffers from contention.

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.

Layout Lock

Data-structures can benefit from dynamic data layout modifications when the size or the shape of the data structure changes during the execution, or when different phases in the program execute different workloads. However, in a modern multi-core environment, layout modifications involve costly synchronization overhead. In this paper we propose a novel layout lock that incurs a negligible overhead for reads and a small overhead for updates of the data structure. We then demonstrate the benefits of layout changes and also the advantages of the layout lock as its supporting synchronization mechanism for two data structures. In particular, we propose a concurrent binary search tree, and a concurrent array set, that benefit from concurrent layout modifications using the proposed layout lock. Experience demonstrates performance advantages and integration simplicity.

A Fast Contention-Friendly Binary Search Tree

This paper presents a fast concurrent binary search tree algorithm. To achieve high performance under contention, the algorithm divides update operations within an eager abstract access that returns rapidly for efficiency reason and a lazy structural adaptation that may be postponed to diminish contention. To achieve high performance under read-only workloads, it features a rebalancing mechanism and guarantees that read-only operations searching for an element execute lock-free. We evaluate the contention-friendly binary search tree using Synchrobench, a benchmark suite to compare synchronization techniques. More specifically, we compare its performance against five state-of-the-art binary search trees that use locks, transactions or compare-and-swap for synchronization on Intel Xeon, AMD Opteron and Oracle SPARC. Our results show that our tree is more efficient than other trees and double the throughput of existing lock-based trees under high contention.

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.

Practical concurrent binary search trees via logical ordering

We present practical, concurrent binary search tree (BST) algorithms that explicitly maintain logical ordering information in the data structure, permitting clean separation from its physical tree layout. We capture logical ordering using intervals, with the property that an item belongs to the tree if and only if the item is an endpoint of some interval. We are thus able to construct efficient, synchronization-free and intuitive lookup operations. We present (i) a concurrent non-balanced BST with a lock-free lookup, and (ii) a concurrent AVL tree with a lock-free lookup that requires no synchronization with any mutating operations, including balancing operations. Our algorithms apply on-time deletion; that is, every request for removal of a node, results in its immediate removal from the tree. This new feature did not exist in previous concurrent internal tree algorithms. We implemented our concurrent BST algorithms and evaluated them against several state-of-the-art concurrent tree algorithms. Our experimental results show that our algorithms with lock-free contains and on-time deletion are practical and often comparable to the state-of-the-art.

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%.

Lock-free implementation of concurrent binary search tree

Lock-free implementation of concurrent binary search tree

A practical concurrent binary search tree

We propose a concurrent relaxed balance AVL tree algorithm that is fast, scales well, and tolerates contention. It is based on optimistic techniques adapted from software transactional memory, but takes advantage of specific knowledge of the the algorithm to reduce overheads and avoid unnecessary retries. We extend our algorithm with a fast linearizable clone operation, which can be used for consistent iteration of the tree. Experimental evidence shows that our algorithm outperforms a highly tuned concurrent skip list for many access patterns, with an average of 39% higher single-threaded throughput and 32% higher multi-threaded throughput over a range of contention levels and operation mixes.