Experiments on Union-Find Algorithms for the Disjoint-Set Data Structure

Patwary, Md. Mostofa Ali; Blair, Jean R. S.; Manne, Fredrik

doi:10.1007/978-3-642-13193-6_35

Cited by 41 publications

(31 citation statements)

References 11 publications

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“…It comes with two main operations: FIND and UNION. The FIND operation determines to which set a given element belongs, while the UNION operation joins two existing sets [22], [28]. Each set is identified by a representative x, which is usually some member of the set.…”

Section: A the Disjoint-set Data Structurementioning

confidence: 99%

“…In this paper, we have used the empirically best known UNION technique, known as Rem's algorithm (a lower indexed root points to a higher indexed root) with the splicing compression technique. Details on these can be found in [22].…”

Section: A the Disjoint-set Data Structurementioning

confidence: 99%

“…, X p } (one for each of the p threads running in parallel) and each thread t owns partition X t . We divide the algorithm into two segments, local computation (Line 2-18) and merging (Line [19][20][21][22][23][24][25]. Both steps run in parallel.…”

Section: A Parallel Dbscan On Shared Memory Computersmentioning

confidence: 99%

“…To overcome the performance bottleneck due to the serialized computation at the master process, we present a fully distributed parallel algorithm that employs the disjoint-set data structure [21], [22], [23], a mechanism to enable higher concurrency for data access while maintaining a comparable time complexity to the classical DBSCAN algorithm. The idea of our approach is as follows.…”

Section: Introductionmentioning

confidence: 99%

“…Otherwise, we call PARALLELUNION(x, P x , y ) to perform a UNION of the trees containing x and y in the distributed-memory architecture. For this we use similar techniques as presented in [22] and [30].…”

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confidence: 99%

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A new scalable parallel DBSCAN algorithm using the disjoint-set data structure

Patwary

Palsetia

Agrawal

et al. 2012

2012 International Conference for High Performance Computing, Networking, Storage and Analysis

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104

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Abstract-DBSCAN is a well-known density based clustering algorithm capable of discovering arbitrary shaped clusters and eliminating noise data. However, parallelization of DBSCAN is challenging as it exhibits an inherent sequential data access order. Moreover, existing parallel implementations adopt a master-slave strategy which can easily cause an unbalanced workload and hence result in low parallel efficiency.We present a new parallel DBSCAN algorithm (PDSDBSCAN) using graph algorithmic concepts. More specifically, we employ the disjoint-set data structure to break the access sequentiality of DBSCAN. In addition, we use a tree-based bottom-up approach to construct the clusters. This yields a better-balanced workload distribution. We implement the algorithm both for shared and for distributed memory.Using data sets containing up to several hundred million high-dimensional points, we show that PDSDBSCAN significantly outperforms the master-slave approach, achieving speedups up to 25.97 using 40 cores on shared memory architecture, and speedups up to 5,765 using 8,192 cores on distributed memory architecture.

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Section: A the Disjoint-set Data Structurementioning

confidence: 99%

Section: A the Disjoint-set Data Structurementioning

confidence: 99%

Section: A Parallel Dbscan On Shared Memory Computersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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A new scalable parallel DBSCAN algorithm using the disjoint-set data structure

Patwary

Palsetia

Agrawal

et al. 2012

2012 International Conference for High Performance Computing, Networking, Storage and Analysis

Self Cite

104

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An efficient analyse phase for element problems

Hogg

Scott

2012

Numerical Linear Algebra App

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The analyse phase of a sparse direct solver for symmetrically structured linear systems of equations is used to determine the sparsity pattern of the matrix factor. This allows the subsequent numerical factorisation and solve phases to be executed efficiently. Many direct solvers require the system matrix to be in assembled form. For problems arising from finite element applications, assembling and then using the system matrix can be costly in terms of both time and memory. This paper describes and implements a variant of the work of Gilbert, Ng and Peyton for matrices in elemental form. The proposed variant works with an equivalent matrix that avoids explicitly assembling the system matrix and exploits supervariables. Numerical experiments using problems from practical applications are used to demonstrate the significant advantages of working directly with the elemental form.In this paper, our aim is to design and implement an efficient analyse phase that can be used in the development of modern sparse direct solvers. Our main interest is in element problems but we want to allow both matrices that are held in assembled form (input by columns) and in elemental form (input by elements). In each case, we want to exploit supervariables (columns of A with the same sparsity pattern) and we want to keep memory bandwidth to a minimum, while not compromising efficiency. Thus, our main contributions are the incorporation of supervariables into the Gilbert, Ng and Peyton [1] approach to the analyse phase for assembled problems and the design and implementation of an efficient analyse phase for elemental problems that avoids explicitly assembling the matrix pattern. Our new analyse phase is available within the HSL software library [2] as package HSL_MC78. We remark that, historically, the analyse phase was much faster than the factorisation phase. Considerable effort has gone into parallelizing the factorisation so that the gap between the times for the two phases has narrowed. It is therefore important that the analyse phase be implemented efficiently to prevent it from becoming a bottleneck.This paper is organised as follows. In the rest of this introduction, we introduce the terms and notation that we will use throughout the paper and we present our test problems and our test environment. Then, in Section 2, we summarise and briefly discuss key algorithms used within the analyse phase. Section 3 focuses on the case when A is in assembled form and looks at efficiently identifying supervariables, incorporating supervariables into constructing the elimination tree and into the column count algorithm of Gilbert, Ng and Peyton [1]; numerical results illustrate the potential savings resulting from exploiting supervariables. In Section 4, we consider how to handle problems in elemental form without explicitly assembling the sparsity pattern of A. Results for problems arising from finite-element applications are presented. Timings for the analyse phase of one of our sparse direct solvers that incorporates our new analyse code a...

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An Efficient Run-Based Connected Component Labeling Algorithm for Processing Holes

Lemaître¹,

Maurice²,

Lacassagne³

2022

Lecture Notes in Computer Science

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This article introduces a new connected component labeling and analysis algorithm framework that is able to compute in one pass the foreground and the background labels as well as the adjacency tree. The computation of features (bounding boxes, first statistical moments, Euler number) is done on-the-fly. The transitive closure enables an efficient hole processing that can be filled while their features are merged with the surrounding connected component without the need to rescan the image. A comparison with State-of-the-Art shows that this new algorithm can do all these computations faster than all existing algorithms processing foreground and background connected components or holes.

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Experiments on Union-Find Algorithms for the Disjoint-Set Data Structure

Cited by 41 publications

References 11 publications

A new scalable parallel DBSCAN algorithm using the disjoint-set data structure

A new scalable parallel DBSCAN algorithm using the disjoint-set data structure

An efficient analyse phase for element problems

An Efficient Run-Based Connected Component Labeling Algorithm for Processing Holes

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