Batch-Parallel Euler Tour Trees

Tseng, Thomas; Dhulipala, Laxman; Blelloch, Guy E.

doi:10.1137/1.9781611975499.8

Cited by 25 publications

(25 citation statements)

References 41 publications

(67 reference statements)

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“…As far as Euler Tour Trees are concerned, Tseng et al designed a batch-parallel ETT algorithm using a phase-concurrent skip-list [20]. Phase-concurrent means that no concurrent operations of different types are allowed.…”

Section: Related Workmentioning

confidence: 99%

“…They get concurrent reads "for free", since they employ immutable data structures. Similarly to Tseng et al [20] and Acar et al [10], they use parallelism to process batches of operations. Nevertheless, in our problem trees should have links both from parents to children and from children to parents, because connectivity queries traverse trees from bottom to top.…”

Section: Related Workmentioning

confidence: 99%

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A Scalable Concurrent Algorithm for Dynamic Connectivity

Федоров¹,

Koval²,

Alistarh

2021

Preprint

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Dynamic Connectivity is a fundamental algorithmic graph problem, motivated by a wide range of applications to social and communication networks and used as a building block in various other algorithms, such as the bi-connectivity and the dynamic minimal spanning tree problems. In brief, we wish to maintain the connected components of graph under dynamic edge insertions and deletions. In the sequential case, the problem has been well-studied from both theoretical and practical perspectives. However, much less is known about efficient concurrent solutions to this problem. This is the gap we address in this paper. We start from one of the classic data structures used to solve this problem, the Euler Tour Tree. Our first contribution is a non-blocking single-writer implementation of it. We leverage this data structure to obtain the first truly concurrent generalization of dynamic connectivity, which preserves the time complexity of its sequential counterpart, but is also scalable in practice. To achieve this, we rely on three main techniques. The first is to ensure that connectivity queries, which usually dominate real-world workloads, are non-blocking. The second non-trivial technique expands the above idea by making all queries that do not change the connectivity structure non-blocking. The third ingredient is applying fine-grained locking for updating the connected components, which allows operations on disjoint components to occur in parallel. We evaluate the resulting algorithm on various workloads, executing on both real and synthetic graphs. The results show the efficiency of each of the proposed optimizations; the most efficient variant improves the performance of a coarse-grained based implementation on realistic scenarios up to 6x on average and up to 30x when connectivity queries dominate.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

A Scalable Concurrent Algorithm for Dynamic Connectivity

Федоров¹,

Koval²,

Alistarh

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…It also supports Extract to return all records with keys within a certain threshold in parallel. The LaB-PQ is inspired by the recent work on batch-dynamic data structures [3,7,18,80,85,87], where multiple updates or queries are applied to the data structure in batches in parallel. One advantage of LaB-PQ is that we do not explicitly generate the batches, but do it lazily.…”

Section: Gapbsmentioning

confidence: 99%

Optimal Parallel Algorithms in the Binary-Forking Model

Blelloch

Fineman

et al. 2020

Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures

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In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference. In the binary-forking model, tasks can only fork into two child tasks, but can do so recursively and asynchronously. The tasks share memory, supporting reads, writes and test-and-sets. Costs are measured in terms of work (total number of instructions), and span (longest dependence chain).The binary-forking model is meant to capture both algorithm performance and algorithm-design considerations on many existing multithreaded languages, which are also asynchronous and rely on binary forks either explicitly or under the covers. In contrast to the widely studied PRAM model, it does not assume arbitrary-way forks nor synchronous operations, both of which are hard to implement in modern hardware. While optimal PRAM algorithms are known for the problems studied herein, it turns out that arbitrary-way forking and strict synchronization are powerful, if unrealistic, capabilities. Natural simulations of these PRAM algorithms in the binary-forking model (i.e., implementations in existing parallel languages) incur an Ω(log n) overhead in span. This paper explores techniques for designing optimal algorithms when limited to binary forking and assuming asynchrony. All algorithms described in this paper are the first algorithms with optimal work and span in the binary-forking model. Most of the algorithms are simple. Many are randomized.

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“…The natural extension, batch dynamic algorithms have also been very recently studied where more than one update arrives per round. Dhulipala et al [5] build on work on the Euler Tour Tree data structure in the parallel setting [1,23], and demonstrate a batch-dynamic connectivity algorithm in the MPC Model using sketching techniques. As of yet, we know of no existing work on the dynamic exact MST problem or the batch-dynamic MST problem.…”

Section: Background and Related Workmentioning

confidence: 99%

How fast can you update your MST? (Dynamic algorithms for cluster computing)

Gilbert,

2020

Preprint

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Imagine a large graph that is being processed by a cluster of computers, e.g., described by the k-machine model or the Massively Parallel Computation Model. The graph, however, is not static; instead it is receiving a constant stream of updates. How fast can the cluster process the stream of updates? The fundamental question we want to ask in this paper is whether we can update the graph fast enough to keep up with the stream.We focus specifically on the problem of maintaining a minimum spanning tree (MST), and we give an algorithm for the k-machine model that can process O(k) graph updates per O(1) rounds with high probability. (And these results carry over to the Massively Parallel Computation (MPC) model.) We also show a lower bound, i.e., it is impossible to process k 1+ϵ updates in O(1) rounds. Thus we provide a nearly tight answer to the question of how fast a cluster can respond to a stream of graph modifications while maintaining an MST.

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Batch-Parallel Euler Tour Trees

Cited by 25 publications

References 41 publications

A Scalable Concurrent Algorithm for Dynamic Connectivity

A Scalable Concurrent Algorithm for Dynamic Connectivity

Optimal Parallel Algorithms in the Binary-Forking Model

How fast can you update your MST? (Dynamic algorithms for cluster computing)

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