Log-Free Concurrent Data Structures

Non-volatile RAM (NVRAM) makes it possible for data structures to tolerate transient failures, assuming however that programmers have designed these structures such that their consistency is preserved upon recovery. Previous ap- proaches are typically transactional and inherently make heavy use of logging, resulting in implementations that are significantly slower than their DRAM counterparts. In this paper, we introduce a set of techniques aimed at lock-free data structures that, in the large majority of cases, remove the need for logging (and costly durable store instructions) both in the data structure algorithm and in the associated memory management scheme. Together, these generic techniques enable us to design what we call log-free concurrent data structures, which, as we illustrate on linked lists, hash tables, skip lists, and BSTs, can provide several-fold performance improvements over previous transaction-based implementations, with overheads of the order of milliseconds for recovery after a failure. We also highlight how our techniques can be integrated into practical systems, by presenting a durable version of Memcached that maintains the performance of its volatile counterpart

A VLSI Architecture for Concurrent Data Structures

Concurrent data structures simplify the development of concurrent programs by encapsulating commonly used mechanisms for synchronization and communication into data structures. This thesis develops a notation for describing concurrent data structures, presents examples of concurrent data structures, and describes an architecture to support concurrent data structures. Concurrent Smalltalk (CST), a derivative of Smalltalk-80 with extensions for concurrency, is developed to describe concurrent data structures. CST allows the programmer to specify objects that are distributed over the nodes of a concurrent computer. These distributed objects have many constituent objects and thus can process many messages simultaneously. They are the foundation upon which concurrent data structures are built. The balanced cube is a concurrent data structure for ordered sets. The set is distributed by a balanced recursive partition that maps to the subcubes of a binary n-cube using a Gray code. A search algorithm, VW search, based on the distance properties of the Gray code, searches a balanced cube in O(log N) time. Because it does not have the root bottleneck that limits all tree-based data structures to O(1) concurrency, the balanced cube achieves O(~og ) concurrency. Considering graphs as concurrent data structures, graph algorithms are presented for the shortest path problem, the mix-flow problem, and graph partitioning. These algorithms introduce new synchronization techniques to achieve better performance than existing algorithms. A message-passing, concurrent architecture is developed that exploits the characteristics of VLSI technology to support concurrent data structures. Interconnection topologies are compared on the basis of dimension. It is shown that minimum latency is achieved with a very low dimensional network. A deadlock-free routing strategy is developed for this class of networks, and a prototype VLSI chip implementing this strategy is described. A message-driven processor complements the network by responding to messages with a very low latency. The processor directly executes messages, eliminating a level of interpretation. To take advantage of the performance offered by specialization while at the same time retaining flexibility, processing elements can be specialized to operate on a single class of objects. These object experts accelerate the performance of all applications using this class

The Lock-free kk-LSM Relaxed Priority Queue

Priority queues are data structures which store keys in an ordered fashion to allow efficient access to the minimal (maximal) key. Priority queues are essential for many applications, e.g., Dijkstra's single-source shortest path algorithm, branch-and-bound algorithms, and prioritized schedulers. Efficient multiprocessor computing requires implementations of basic data structures that can be used concurrently and scale to large numbers of threads and cores. Lock-free data structures promise superior scalability by avoiding blocking synchronization primitives, but the \emph{delete-min} operation is an inherent scalability bottleneck in concurrent priority queues. Recent work has focused on alleviating this obstacle either by batching operations, or by relaxing the requirements to the \emph{delete-min} operation. We present a new, lock-free priority queue that relaxes the \emph{delete-min} operation so that it is allowed to delete \emph{any} of the $\rho+1$ smallest keys, where $\rho$ is a runtime configurable parameter. Additionally, the behavior is identical to a non-relaxed priority queue for items added and removed by the same thread. The priority queue is built from a logarithmic number of sorted arrays in a way similar to log-structured merge-trees. We experimentally compare our priority queue to recent state-of-the-art lock-free priority queues, both with relaxed and non-relaxed semantics, showing high performance and good scalability of our approach.Comment: Short version as ACM PPoPP'15 poste

A method for implementing lock-free shared data structures

We are interested in implementing data structures on shared memory multiprocessors. A natural model for these machines is an asynchronous parallel machine, in which the processors are subject to arbitrary delays. On such machines, it is desirable for algorithms to be {\em lock-free}, that is, they must allow concurrent access to data without using mutual exclusion. Efficient lock-free implementations are known for some specific data structures, but these algorithms do not generalize well to other structures. For most data structures, the only previously known lock-free algorithm is due to Herlihy. Herlihy presents a simple methodology to create a lock-free implementation of a general data structure, but his approach can be very expensive. We present a technique that provides the semantics of exclusive access to data without using mutual exclusion. Using this technique, we devise the {\em caching method}, a general method of implementing lock-free data structures that is provably better than Herlihy's methodology for many well-known data structures. The cost of one operation using the caching method is proportional to $T \log T$, where $T$ is the sequential cost of the operation. Under Herlihy's methodology, the cost is proportional to $T + C$, where $C$ is the time needed to make a logical copy of the data structure. For many data structures, such as arrays and {\em well connected} pointer-based structures (e.g., a doubly linked list), the best known value for $C$ is proportional to the size of the structure, making the copying time much larger than the sequential cost of an operation. The new method can also allow {\em concurrent updates} to the data structure; Herlihy's methodology cannot. A correct lock-free implementation can be derived from a correct sequential implementation in a straightforward manner using this method. The method is also flexible; a programmer can change many of the details of the default implementation to optimize for a particular pattern of data structure use

The SkipTrie: low-depth concurrent search without rebalancing

To date, all concurrent search structures that can support predecessor queries have had depth logarithmic in m, the number of elements. This paper introduces the SkipTrie, a new concurrent search structure supporting predecessor queries in amortized expected O(log log u + c) steps, insertions and deletions in O(c log log u), and using O(m) space, where u is the size of the key space and c is the contention during the recent past. The SkipTrie is a probabilistically-balanced version of a y-fast trie consisting of a very shallow skiplist from which randomly chosen elements are inserted into a hash-table based x-fast trie. By inserting keys into the x-fast-trie probabilistically, we eliminate the need for rebalancing, and can provide a lock-free linearizable implementation. To the best of our knowledge, our proof of the amortized expected performance of the SkipTrie is the first such proof for a tree-based data structure.National Science Foundation (U.S.) (Grant CCF-1217921)United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Grant ER26116/DE-SC0008923)Oracle CorporationIntel Corporatio

The Balanced Cube: A Concurrent Data Structure

This paper describee the balanced cube, a new data structure for implementing ordered seta. Conventional dats structures such as heaps, balanced trees and B-trees have root bottlenecks which limit their potential concurrency and make them unable to take advantage of the computing potential of concurrent machines. The balanced cube achieves greater concurrency by eliminating the root bottleneck; an operation in the balanced cube can be initiated from any node. The throughput of the balanced cube on a concurrent computer is O times O/Log N compared with O(1) for a conventional data structure. Operations on the balanced cube are shown to be deadlock free and consistent with a sequential execution ordered by completion time

DeltaTree: A Practical Locality-aware Concurrent Search Tree

As other fundamental programming abstractions in energy-efficient computing, search trees are expected to support both high parallelism and data locality. However, existing highly-concurrent search trees such as red-black trees and AVL trees do not consider data locality while existing locality-aware search trees such as those based on the van Emde Boas layout (vEB-based trees), poorly support concurrent (update) operations. This paper presents DeltaTree, a practical locality-aware concurrent search tree that combines both locality-optimisation techniques from vEB-based trees and concurrency-optimisation techniques from non-blocking highly-concurrent search trees. DeltaTree is a $k$-ary leaf-oriented tree of DeltaNodes in which each DeltaNode is a size-fixed tree-container with the van Emde Boas layout. The expected memory transfer costs of DeltaTree's Search, Insert, and Delete operations are $O(\log_B N)$, where $N, B$ are the tree size and the unknown memory block size in the ideal cache model, respectively. DeltaTree's Search operation is wait-free, providing prioritised lanes for Search operations, the dominant operation in search trees. Its Insert and {\em Delete} operations are non-blocking to other Search, Insert, and Delete operations, but they may be occasionally blocked by maintenance operations that are sometimes triggered to keep DeltaTree in good shape. Our experimental evaluation using the latest implementation of AVL, red-black, and speculation friendly trees from the Synchrobench benchmark has shown that DeltaTree is up to 5 times faster than all of the three concurrent search trees for searching operations and up to 1.6 times faster for update operations when the update contention is not too high

Non-blocking Priority Queue based on Skiplists with Relaxed Semantics

Priority queues are data structures that store information in an orderly fashion. They are of tremendous importance because they are an integral part of many applications, like Dijkstra’s shortest path algorithm, MST algorithms, priority schedulers, and so on. Since priority queues by nature have high contention on the delete_min operation, the design of an efficient priority queue should involve an intelligent choice of the data structure as well as relaxation bounds on the data structure. Lock-free data structures provide higher scalability as well as progress guarantee than a lock-based data structure. That is another factor to be considered in the priority queue design. We present a relaxed non-blocking priority queue based on skiplists. We address all the design issues mentioned above in our priority queue. Use of skiplists allows multiple threads to concurrently access different parts of the skiplist quickly, whereas relaxing the priority queue delete_min operation distributes contention over the skiplist instead of just at the front. Furthermore, a non-blocking implementation guarantees that the system will make progress even when some process fails. Our priority queue is internally composed of several priority queues, one for each thread and one shared priority queue common to all threads. Each thread selects the best value from its local priority queue and the shared priority queue and returns the value. In case a thread is unable to delete an item, it tries to spy items from other threads\u27 local priority queues. We experimentally and theoretically show the correctness of our data structure. We also compare the performance of our data structure with other variations like priority queues based on coarse-grained skiplists for both relaxed and non-relaxed semantics

The Power of Choice in Priority Scheduling

Consider the following random process: we are given $n$ queues, into which elements of increasing labels are inserted uniformly at random. To remove an element, we pick two queues at random, and remove the element of lower label (higher priority) among the two. The cost of a removal is the rank of the label removed, among labels still present in any of the queues, that is, the distance from the optimal choice at each step. Variants of this strategy are prevalent in state-of-the-art concurrent priority queue implementations. Nonetheless, it is not known whether such implementations provide any rank guarantees, even in a sequential model. We answer this question, showing that this strategy provides surprisingly strong guarantees: Although the single-choice process, where we always insert and remove from a single randomly chosen queue, has degrading cost, going to infinity as we increase the number of steps, in the two choice process, the expected rank of a removed element is $O( n )$ while the expected worst-case cost is $O( n \log n )$. These bounds are tight, and hold irrespective of the number of steps for which we run the process. The argument is based on a new technical connection between "heavily loaded" balls-into-bins processes and priority scheduling. Our analytic results inspire a new concurrent priority queue implementation, which improves upon the state of the art in terms of practical performance