A design of a parallel dictionary using skip lists

Gabarró, Joaquim; Martínez, Conrado; Messeguer, Xavier

doi:10.1016/0304-3975(94)00288-6

Cited by 10 publications

(7 citation statements)

References 18 publications

(30 reference statements)

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“…They allow all operations to run concurrently and do not show theoretical bounds. Gabarró et al present a skip list supporting batch searches, insertions, or deletions in O(k(log n + log k)) expected work and O(log n + log k) expected depth [18].…”

Section: Sequencesmentioning

confidence: 99%

Batch-Parallel Euler Tour Trees

Tseng¹,

Dhulipala²,

Blelloch³

2019

2019 Proceedings of the Twenty-First Workshop on Algorithm Engineering and Experiments (ALENEX)

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The dynamic trees problem is to maintain a forest undergoing edge insertions and deletions while supporting queries for information such as connectivity. There are many existing data structures for this problem, but few of them are capable of exploiting parallelism in the batch setting, in which large batches of edges are inserted or deleted from the forest at once. In this paper, we demonstrate that the Euler tour tree, an existing sequential dynamic trees data structure, can be parallelized in the batch setting. For a batch of k updates over a forest of n vertices, our parallel Euler tour trees achieve O(k log(1 + n/k)) expected work and O(log n) depth with high probability. Our work bound is asymptotically optimal, and we improve on the depth bound achieved by Acar et al. for the batch-parallel dynamic trees problem [1].Our main building block for parallelizing Euler tour trees is a batch-parallel skip list data structure, which we believe may be of independent interest. Euler tour trees require a sequence data structure capable of joins and splits. Traditionally, balanced binary trees are used, but they are difficult to join or split in parallel when processing batches of updates. We show that skip lists, on the other hand, support batches of joins or splits of size k over n elements with O(k log(1 + n/k)) work in expectation and O(log n) depth with high probability. We also achieve the same efficiency bounds for augmented skip lists, which allows us to augment our Euler tour trees to support subtree queries.Our data structures achieve between 67-96× self-relative speedup on 72 cores with hyperthreading on large batch sizes.

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Section: Sequencesmentioning

confidence: 99%

Batch-Parallel Euler Tour Trees

Tseng¹,

Dhulipala²,

Blelloch³

2019

2019 Proceedings of the Twenty-First Workshop on Algorithm Engineering and Experiments (ALENEX)

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“…We consider the insertion case where we h a ve a n A VL tree with n keys and we h a ve to insert an ordered set of k new keys stored in the array a 1::k]. First, we employ the search algorithm by p a c ket routing 8,3,2]. This search algorithm is formally identical to the search b y p a c ket routing on Skip lists.…”

Section: Parallel Insertion Algorithmmentioning

confidence: 99%

“…The results about read con icts in Skip lists apply here 2] and, at most three subpackets can remain on a node. When the subpackets are located at the bottom of the AVL, the divide and conquer approach g i v en in 8] allows us to start a pipeline of waves as in (2). When all red nodes have become white, the red relaxed AVL tree is an AVL tree and the following theorem holds: Theorem 2 The massively parallel insertion of k keys into an AVL tree w i t h n keys takes time O(log n + log k) using k processors on an EREW PRAM.…”

Section: Parallel Insertion Algorithmmentioning

confidence: 99%

“…20244 (AL-COM IT) and DGICYT under grant PB95-0787 (project KOALA) and CICIT TIC97-1475-CE and CIRIT 1997SGR-00366. 2 Expanded version of a talk presented at the 9th International Conference on Parallel and Distributed Computing Systems, ISCA, 1996. all the internal nodes have 2 or 3 sons and all the leaves have the same depth. We assume that any leaf has two nil nodes as left and right sons.…”

Section: Introductionmentioning

confidence: 99%

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Parallel dictionaries with local rules on AVL and brother trees

Gabarró

Messeguer

1998

Information Processing Letters

Self Cite

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We present a set of local rules to deal with dictionaries. Their main advantage is that they can be scheduled in a highly synchronized way to get parallel dictionaries on AVL trees. Up to now trees used in massively parallel dictionaries needed to have all the leaves at the same depth, such as 2{3 trees. Therefore, it was possible (in insertions and deletions) the bottom-up reconstruction of the tree in a very regular fashion, as a pipeline of plane waves moving up. On AVL trees the situation looks di erent because leaves can have di erent depth, therefore any w ave i n a pipeline is highly irregular. To solve this problem we de ne virtual plane waves allowing us to develop an EREW dictionary for k keys with k processors and time O(log n + log k). Later on we generalize the sequential algorithms on brother trees presented by Ottmann and Wood in the same way.

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“…The performance of the Binary Search Tree (BT), a widely used structure, deteriorates signi"cantly to almost O(n) when the structure is created by ordered, partially ordered or skewed input data sets [1,5,6]. In realistic settings, such data sets appear often [7][8][9][10]. To prevent poor response time, various other classes of trees have been proposed, based on height balance.…”

Section: Introductionmentioning

confidence: 99%

Contemporary Access Structures Under Mixed Workloads

Delis

LeViet

1997

The Computer Journal

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Modern high-performance computing systems and databases are implemented under the assumption that a very large proportion of the data used can now be maintained in volatile memory. In this paper, we compare experimentally two recently proposed self-adjusting access structures that can be used to organize data in such settings, namely, the Skip-List (SL) and the Binary B-Tree (BB-Tree). We examine the scalability of these two methods against both mixed and pure-query workloads. Our experiments reveal the behaviour of SLs and BB-Trees under diverse environments and varying data requirements.

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A design of a parallel dictionary using skip lists

Cited by 10 publications

References 18 publications

Batch-Parallel Euler Tour Trees

Batch-Parallel Euler Tour Trees

Parallel dictionaries with local rules on AVL and brother trees

Contemporary Access Structures Under Mixed Workloads

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