GPU Accelerated Maximum Cardinality Matching Algorithms for Bipartite Graphs

Deveci, Mehmet; Kaya, Kamer; Uçar, Bora; Çatalyürek, Ümit V.

doi:10.1007/978-3-642-40047-6_84

Cited by 13 publications

(14 citation statements)

References 19 publications

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“…The running time of the proposed implementations are compared against the sequential PR implementation (PR) [5], the multicore parallel implementations P-DBFS [13], and a GPU implementation of HKDW [14]. For the sequential PR implementation, we tried a set of k values to set the frequency of global-relabeling to k × (m + n).…”

Section: Methodsmentioning

confidence: 99%

“…In recent work, we designed and developed atomic-free GPU implementations, G-HK and G-HKDW [14], corresponding to two augmenting-path-based algorithms, HK [18] and HKDW [19]. HK has the best known worst-case running time complexity of O(τ √ n + m) for a bipartite graph with τ edges.…”

Section: Parallel Algorithms For Bipartite Cardinality Matchingsmentioning

confidence: 99%

“…HKDW performs another set of DFS-based searches to augment using the remaining unmatched rows. In this paper, we compare the performance of the proposed algorithm with that of G-HKDW which performed better than G-HK [14].…”

Section: Parallel Algorithms For Bipartite Cardinality Matchingsmentioning

confidence: 99%

“…Azad et al [13] introduce several multicore implementations of the maximum cardinality matching algorithms on bipartite graphs. In a recent study [14], we investigated the performance of augmentingpath-based approach on GPU architectures.…”

Section: Introductionmentioning

confidence: 99%

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A Push-Relabel-Based Maximum Cardinality Bipartite Matching Algorithm on GPUs

Deveci¹,

Kaya²,

Uçar

et al. 2013

2013 42nd International Conference on Parallel Processing

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Abstract-We design, develop, and evaluate an atomic-and lock-free GPU implementation of the push-relabel algorithm in the context of finding maximum cardinality matchings in bipartite graphs. The problem has applications on computer science, scientific computing, bioinformatics, and other areas. Although the GPU parallelization of the push-relabel technique has been investigated in the context of flow algorithms, to the best of our knowledge, ours is the first study which focuses on the maximum cardinality matching. We compare the proposed algorithms with serial, multicore, and manycore bipartite graph matching implementations from the literature on a large set of real-life problems. Our experiments show that the proposed pushrelabel-based GPU algorithm is faster than the existing parallel and sequential implementations.

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Section: Methodsmentioning

confidence: 99%

Section: Parallel Algorithms For Bipartite Cardinality Matchingsmentioning

confidence: 99%

Section: Parallel Algorithms For Bipartite Cardinality Matchingsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Push-Relabel-Based Maximum Cardinality Bipartite Matching Algorithm on GPUs

Deveci¹,

Kaya²,

Uçar

et al. 2013

2013 42nd International Conference on Parallel Processing

Self Cite

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“…We address some of the performance issues raised by them in our work. In a similar vein, Devici et al also present adaptation of maximum matching on GPUs [3].…”

Section: Related Workmentioning

confidence: 99%

Optimizing Approximate Weighted Matching on Nvidia Kepler K40

Naim

Manne

Halappanavar

et al. 2015

2015 IEEE 22nd International Conference on High Performance Computing (HiPC)

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Matching is a fundamental graph problem with numerous applications in science and engineering. While algorithms for computing optimal matchings are difficult to parallelize, approximation algorithms on the other hand generally compute high quality solutions and are amenable to parallelization. In this paper, we present efficient implementations of the current best algorithm for half-approximate weighted matching, the Suitor algorithm, on Nvidia Kepler K-40 platform. We develop four variants of the algorithm that exploit hardware features to address key challenges for a GPU implementation. We also experiment with different combinations of work assigned to a warp. Using an exhaustive set of 269 inputs, we demonstrate that the new implementation outperforms the previous best GPU algorithm by 10 to 100× for over 100 instances, and from 100 to 1000× for 15 instances. We also demonstrate up to 20× speedup relative to 2 threads, and up to 5× relative to 16 threads on Intel Xeon platform with 16 cores for the same algorithm. The new algorithms and implementations provided in this paper will have a direct impact on several applications that repeatedly use matching as a key compute kernel. Further, algorithm designs and insights provided in this paper will benefit other researchers implementing graph algorithms on modern GPU architectures.

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On the use of suboptimal matchings for scaling and ordering sparse symmetric matrices

Hogg

Scott

2015

Numerical Linear Algebra App

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SUMMARYThe use of matchings is a powerful technique for scaling and ordering sparse matrices prior to the solution of a linear system Ax D b. Traditional methods such as implemented by the HSL software package MC64 use the Hungarian algorithm to solve the maximum weight maximum cardinality matching problem. However, with advances in the algorithms and hardware used by direct methods for the parallelization of the factorization and solve phases, the serial Hungarian algorithm can represent an unacceptably large proportion of the total solution time for such solvers. Recently, auction algorithms and approximation algorithms have been suggested as alternatives for achieving near-optimal solutions for the maximum weight maximum cardinality matching problem. In this paper, the efficacy of auction and approximation algorithms as replacements for the Hungarian algorithm is assessed in the context of sparse symmetric direct solvers when used in problems arising from a range of practical applications. High-cardinality suboptimal matchings are shown to be as effective as optimal matchings for the purposes of scaling. However, matching-based ordering techniques require that matchings are much closer to optimality before they become effective. The auction algorithm is demonstrated to be capable of finding such matchings significantly faster than the Hungarian algorithm, but our 1 2 -approximation matching approach fails to consistently achieve a sufficient cardinality.

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GPU Accelerated Maximum Cardinality Matching Algorithms for Bipartite Graphs

Cited by 13 publications

References 19 publications

A Push-Relabel-Based Maximum Cardinality Bipartite Matching Algorithm on GPUs

A Push-Relabel-Based Maximum Cardinality Bipartite Matching Algorithm on GPUs

Optimizing Approximate Weighted Matching on Nvidia Kepler K40

On the use of suboptimal matchings for scaling and ordering sparse symmetric matrices

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