A Comparison of Relativistic and Reader-Writer Locking Approaches to Shared Data Access

This paper explores the relationship between reader-writer locking and relativistic programming approaches to managing accesses to shared data. It demonstrates that by placing certain restrictions on writers, relativistic programming allows more concurrency than reader-writer locking while still providing the same isolation guarantees. Relativistic programming also allows for a straightforward model for reasoning about the correctness of programs that allow concurrent read-write accesses

A Pedagogically Sound yet Efficient Deletion algorithm for Red-Black Trees: The Parity-Seeking Delete Algorithm

Red-black (RB) trees are one of the most efficient variants of balanced binary search trees. However, they have always been blamed for being too complicated, hard to explain, and not suitable for pedagogical purposes. Sedgewick (2008) proposed left-leaning red-black (LLRB) trees in which red links are restricted to left children, and proposed recursive concise insert and delete algorithms. However, the top-down deletion algorithm of LLRB is still very complicated and highly inefficient. In this paper, we first consider 2-3 red-black trees in which both children cannot be red. We propose a parity-seeking delete algorithm with the basic idea of making the deficient subtree on a par with its sibling: either by fixing the deficient subtree or by making the sibling deficient, as well, ascending deficiency to the parent node. This is the first pedagogically sound algorithm for the delete operation in red-black trees. Then, we amend our algorithm and propose a parity-seeking delete algorithm for classical RB trees. Our experiments show that, despite having more rotations, 2-3 RB trees are almost as efficient as RB trees and twice faster than LLRB trees. Besides, RB trees with the proposed parity-seeking delete algorithm have the same number of rotations and almost identical running time as the classic delete algorithm. While being extremely efficient, the proposed parity-seeking delete algorithm is easily understandable and suitable for pedagogical purposes

Deletion without Rebalancing in Non-Blocking Binary Search Trees

We present a provably linearizable and lock-free relaxed AVL tree called the non-blocking ravl tree. At any time, the height of a non-blocking ravl tree is upper bounded by log_d (2m) + c, where d is the golden ratio, m is the total number of successful INSERT operations performed so far and c is the number of active concurrent processes that have inserted new keys and are still rebalancing the tree at this time. The most significant feature of the non-blocking ravl tree is that it does not rebalance itself after DELETE operations. Instead, it performs rebalancing only after INSERT operations. Thus, the non-blocking ravl tree is much simpler to implement than other self-balancing concurrent binary search trees (BSTs) which typically introduce a large number of rebalancing cases after DELETE operations, while still providing a provable non-trivial bound on its height. We further conduct experimental studies to compare our solution with other state-of-the-art concurrent BSTs using randomly generated data sequences under uniform distributions, and find that our solution achieves the best performance among concurrent self-balancing BSTs. As the keys in access sequences are likely to be partially sorted in system software, we also conduct experiments using data sequences with various degrees of presortedness to better simulate applications in practice. Our experimental results show that, when there are enough degrees of presortedness, our solution achieves the best performance among all the concurrent BSTs used in our studies, including those that perform self-balancing operations and those that do not, and thus is potentially the best candidate for many real-world applications

Concurrent Lazy Splay Tree with Relativistic Programming Approach

A splay tree is a self-adjusting binary search tree in which recently accessed elements are quick to access again. Splay operation causes the sequential bottleneck at the root of the tree in concurrent environment. The Lazy splaying is to rotate the tree at most one per access so that very frequently accessed item does full splaying. We present the RCU (Read-copy-update) based synchronization mechanism for splay tree operations which allows reads to occur concurrently with updates such as deletion and restructuring by splay rotation. This approach is generalized as relativistic programming. The relativistic programming is the programming technique for concurrent shared-memory architectures which tolerates different threads seeing events occurring in different orders, so that events are not necessarily globally ordered, but rather subject to constraints of per-thread ordering. The main idea of the algorithm is that the update operations are carried out concurrently with traversals/reads. Each update is carried out for new reads to see the new state, while allowing pre-existing reads to proceed on the old state. Then the update is completed after all pre-existing reads have completed

Relativistic red-black trees

Operating system performance and scalability on sharedmemory many-core systems depends critically on efficient access to shared data structures. Scalability has proven difficult to achieve for many data structures. In this paper we present a novel and highly scalable concurrent red-black tree. Red-black trees are widely used in operating systems, but typically exhibit poor scalability. Our red-black tree has linear read scalability, uncontended read performance that is at least 25 % faster than other known approaches, and deterministic lookup times for a given tree size, making it suitable for realtime applications

Generalized Construction of Scalable Concurrent Data Structures via Relativistic Programming

We present relativistic programming, a concurrent programming model based on shared addressing, which supports efficient, scalable operation on either uniform shared-memory or distributed shared- memory systems. Relativistic programming provides a strong causal ordering property, allowing a series of read operations to appear as an atomic transaction that occurs entirely between two ordered write operations. This preserves the simple immutable-memory programming model available via mutual exclusion or transactional memory. Furthermore, relativistic programming provides joint-access parallelism, allowing readers to run concurrently with a writer on the same data. We demonstrate a generalized construction technique for concurrent data structures based on relativistic programming, taking into account the natural orderings provided by reader traversals and writer program order. Our construction technique specifies the precise placement of memory barriers and synchronization operations. To demonstrate our generalized approach, we reconstruct the algorithms for existing relativistic data structures, replacing the algorithm-specific reasoning with our systematic and rigorous construction. Benchmarks of the resulting relativistic read algorithms demonstrate high performance and linear scalability: relativistic resizable hash-tables demonstrate 56% better lookup performance than the current state of the art in Linux, and relativistic red-black trees show 2.5x better lookup performance than transactional memory