Communication-avoiding parallel minimum cuts and connected components

Gianinazzi, Lukas; Kalvoda, Pavel; Palma, Alessandro De; Besta, Maciej; Hoefler, Torsten

doi:10.1145/3178487.3178504

Cited by 16 publications

(19 citation statements)

References 39 publications

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“…We therefore did not further investigate using ILP formulations to solve the minimum cut problem. Finally, we note that the MPI-parallel implementation of KS by Gianinazzi et al [75] finds the minimum cut of RMAT graphs with n =16 000 and an average degree of 4 000 in 5 seconds using 1 536 cores [75]. This is significantly slower than our VieCut algorithm, which finds the minimum cut on a similar-sized RMAT graph [113] in 0.2 seconds using just 24 threads.…”

Section: Algorithmsmentioning

confidence: 80%

“…The Õ() notation ignores logarithmic factors. Gianinazzi et al [75] give a parallel implementation of the algorithm of Karger and Stein. Other than that, there are no parallel implementation of either algorithm known to us. More recently, the randomized contraction-based algorithm of Ghaffari et al [74] solves the minimum cut problem on unweighted graphs in O(m log n) or O m + n log 3 n .…”

Section: Related Workmentioning

confidence: 99%

“…While there are implementations of the algorithm of Karger and Stein [37,75] for the minimum cut problem, to the best of our knowledge there are no published implementations of either of the algorithms to find the cactus graph representing all minimum cuts.…”

Section: Finding All Global Minimum Cutsmentioning

confidence: 99%

See 2 more Smart Citations

Practical Minimum Cut Algorithms

Henzinger

Noe

Schulz

et al. 2018

ACM J. Exp. Algorithmics

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The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our algorithm is based on cluster contraction using label propagation and Padberg and Rinaldi's contraction heuristics [SIAM Review, 1991]. We give both sequential and shared-memory parallel implementations of our algorithm. Extensive experiments on both real-world and generated instances show that our algorithm finds the optimal cut on nearly all instances significantly faster than other state-of-the-art algorithms while our error rate is lower than that of other heuristic algorithms. In addition, our parallel algorithm shows good scalability.

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Section: Algorithmsmentioning

confidence: 80%

Section: Related Workmentioning

confidence: 99%

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Practical Minimum Cut Algorithms

Henzinger

Noe

Schulz

et al. 2018

ACM J. Exp. Algorithmics

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show abstract

“…Ballard et al [45] present an extensive collection of linear algebra algorithms. Moreover, a large body of work exists for minimizing communication in irregular algorithms [46,47], such as Betweenness Centrality [5], min cuts [48], BFS [49], matchings [50], vertex similarity coefficients [51], or general graph computations [52,53,53]. Many of them use linear algebra based formulations [54].…”

Section: Related Workmentioning

confidence: 99%

Pebbles, Graphs, and a Pinch of Combinatorics: Towards Tight I/O Lower Bounds for Statically Analyzable Programs

Kwasniewski,

Ben-Nun,

Gianinazzi

et al. 2021

Preprint

Self Cite

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Determining I/O lower bounds is a crucial step in obtaining communication-efficient parallel algorithms, both across the memory hierarchy and between processors. Current approaches either study specific algorithms individually, disallow programmatic motifs such as recomputation, or produce asymptotic bounds that exclude important constants. We propose a novel approach for obtaining precise I/O lower bounds on a general class of programs, which we call Simple Overlap Access Programs (SOAP). SOAP analysis covers a wide variety of algorithms, from ubiquitous computational kernels to full scientific computing applications. Using the red-blue pebble game and combinatorial methods, we are able to bound the I/O of the SOAP-induced Computational Directed Acyclic Graph (CDAG), taking into account multiple statements, input/output reuse, and optimal tiling. To deal with programs that are outside of our representation (e.g., non-injective access functions), we describe methods to approximate them with SOAP. To demonstrate our method, we analyze 38 different applications, including kernels from the Polybench benchmark suite, deep learning operators, and -for the first time -applications in unstructured physics simulations, numerical weather prediction stencil compositions, and full deep neural networks. We derive tight I/O bounds for several linear algebra kernels, such as Cholesky decomposition, improving the existing reported bounds by a factor of two. For stencil applications, we improve the existing bounds by a factor of up to 14. We implement our method as an open-source tool, which can derive lower bounds directly from provided C code.

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“…Using the techniques of Karger and Stein the algorithm can trivially give the cactus representation of all minimum cuts in O n 2 log n . While there are multiple implementations of the algorithm of Karger and Stein [12,21,28] for the minimum cut problem, to the best of our knowledge there are no published implementations of either of the algorithms to find the cactus graph representing all minimum cuts(with or without data reduction techniques).…”

Section: Introductionmentioning

confidence: 99%

Finding All Global Minimum Cuts In Practice

Henzinger¹,

Noe²,

Schulz³

et al. 2020

Preprint

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We present a practically efficient algorithm that finds all global minimum cuts in huge undirected graphs. Our algorithm uses a multitude of kernelization rules to reduce the graph to a small equivalent instance and then finds all minimum cuts using an optimized version of the algorithm of Nagamochi, Nakao and Ibaraki. In shared memory we are able to find all minimum cuts of graphs with up to billions of edges and millions of minimum cuts in a few minutes. We also give a new linear time algorithm to find the most balanced minimum cuts given as input the representation of all minimum cuts. ACM Subject ClassificationMathematics of computing → Paths and connectivity problems; Mathematics of computing → Graph algorithms; Mathematics of computing → Network flows

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Communication-avoiding parallel minimum cuts and connected components

Cited by 16 publications

References 39 publications

Practical Minimum Cut Algorithms

Practical Minimum Cut Algorithms

Pebbles, Graphs, and a Pinch of Combinatorics: Towards Tight I/O Lower Bounds for Statically Analyzable Programs

Finding All Global Minimum Cuts In Practice

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