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Register a new userAnalyzing the Performance of Lock-Free Data Structures: A Conflict-based Model
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Paul Renaud-Goud
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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This paper considers the modeling and the analysis of the performance of lock-free concurrent data structures. Lock-free designs employ an optimistic conflict control mechanism, allowing several processes to access the shared data object at the same time. They guarantee that at least one concurrent operation finishes in a finite number of its own steps regardless of the state of the operations. Our analysis considers such lock-free data structures that can be represented as linear combinations of fixed size retry loops. Our main contribution is a new way of modeling and analyzing a general class of lock-free algorithms, achieving predictions of throughput that are close to what we observe in practice. We emphasize two kinds of conflicts that shape the performance: (i) hardware conflicts, due to concurrent calls to atomic primitives; (ii) logical conflicts, caused by simultaneous operations on the shared data structure. We show how to deal with these hardware and logical conflicts separately, and how to combine them, so as to calculate the throughput of lock-free algorithms. We propose also a common framework that enables a fair comparison between lock-free implementations by covering the whole contention domain, together with a better understanding of the performance impacting factors. This part of our analysis comes with a method for calculating a good back-off strategy to finely tune the performance of a lock-free algorithm. Our experimental results, based on a set of widely used concurrent data structures and on abstract lock-free designs, show that our analysis follows closely the actual code behavior.
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This paper considers the modelling and the analysis of the performance of lock-free concurrent search data structures. Our analysis considers such lock-free data structures that are utilized through a sequence of operations which are generated with a memoryless and stationary access pattern. Our main contribution is a new way of analysing lock-free search data structures: our execution model matches with the behavior that we observe in practice and achieves good throughput predictions. Search data structures are formed of linked basic blocks, usually referred as nodes, that can be accessed by two kinds of events, characterized by their latencies; (i) CAS events originated as a result of modifications of the search data structures (ii) Read events originated during traversals. This type of data structures are usually designed to accommodate a large number of data nodes, which makes the occurrence of an event on a given node rare at any given time. The throughput is defined by the number of events per operation in conjunction with the factors that impact the latencies of these events. We frame these impacting factors under capacity and coherence cache misses. In this context, we model the events as Poisson processes that we can merge and split to estimate the latencies of the events based on the interleaving of events from different threads, and in turn estimate the throughput. We have validated our analysis on several fundamental lock-free search data structures such as linked lists, hash tables, skip lists and binary trees.
Concurrent data structures are the data sharing side of parallel programming. Data structures give the means to the program to store data, but also provide operations to the program to access and manipulate these data. These operations are implemented through algorithms that have to be efficient. In the sequential setting, data structures are crucially important for the performance of the respective computation. In the parallel programming setting, their importance becomes more crucial because of the increased use of data and resource sharing for utilizing parallelism. The first and main goal of this chapter is to provide a sufficient background and intuition to help the interested reader to navigate in the complex research area of lock-free data structures. The second goal is to offer the programmer familiarity to the subject that will allow her to use truly concurrent methods.
Matrix computations, especially iterative PDE solving (and the sparse matrix vector multiplication subproblem within) using conjugate gradient algorithm, and LU/Cholesky decomposition for solving system of linear equations, form the kernel of many applications, such as circuit simulators, computational fluid dynamics or structural analysis etc. The problem of designing approaches for parallelizing these computations, to get good speedups as much as possible as per Amdahls law, has been continuously researched upon. In this paper, we discuss approaches based on the use of finite projective geometry graphs for these two problems. For the problem of conjugate gradient algorithm, the approach looks at an alternative data distribution based on projective-geometry concepts. It is proved that this data distribution is an optimal data distribution for scheduling the main problem of dense matrix-vector multiplication. For the problem of parallel LU/Cholesky decomposition of general matrices, the approach is motivated by the recently published scheme for interconnects of distributed systems, perfect difference networks. We find that projective-geometry based graphs indeed offer an exciting way of parallelizing these computations, and in fact many others. Moreover, their applications ranges from architectural ones (interconnect choice) to algorithmic ones (data distributions).
Linials famous color reduction algorithm reduces a given $m$-coloring of a graph with maximum degree $Delta$ to a $O(Delta^2log m)$-coloring, in a single round in the LOCAL model. We show a similar result when nodes are restricted to choose their color from a list of allowed colors: given an $m$-coloring in a directed graph of maximum outdegree $beta$, if every node has a list of size $Omega(beta^2 (log beta+loglog m + log log |mathcal{C}|))$ from a color space $mathcal{C}$ then they can select a color in two rounds in the LOCAL model. Moreover, the communication of a node essentially consists of sending its list to the neighbors. This is obtained as part of a framework that also contains Linials color reduction (with an alternative proof) as a special case. Our result also leads to a defective list coloring algorithm. As a corollary, we improve the state-of-the-art truly local $(deg+1)$-list coloring algorithm from Barenboim et al. [PODC18] by slightly reducing the runtime to $O(sqrt{DeltalogDelta})+log^* n$ and significantly reducing the message size (from huge to roughly $Delta$). Our techniques are inspired by the local conflict coloring framework of Fraigniaud et al. [FOCS16].
We present CYCLADES, a general framework for parallelizing stochastic optimization algorithms in a shared memory setting. CYCLADES is asynchronous during shared model updates, and requires no memory locking mechanisms, similar to HOGWILD!-type algorithms. Unlike HOGWILD!, CYCLADES introduces no conflicts during the parallel execution, and offers a black-box analysis for provable speedups across a large family of algorithms. Due to its inherent conflict-free nature and cache locality, our multi-core implementation of CYCLADES consistently outperforms HOGWILD!-type algorithms on sufficiently sparse datasets, leading to up to 40% speedup gains compared to the HOGWILD! implementation of SGD, and up to 5x gains over asynchronous implementations of variance reduction algorithms.
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