MASTIFF: Structure-Aware Minimum Spanning Tree/Forest – ICS’22

36th ACM International Conference on Supercomputing 2022
June 27-30, 2022
Acceptance Rate: 25%

DOI: 10.1145/3524059.3532365
Authors’ Copy (PDF Format)

The Minimum Spanning Forest (MSF) problem finds usage in many different applications. While theoretical analysis shows that linear-time solutions exist, in practice, parallel MSF algorithms remain computationally demanding due to the continuously increasing size of data sets.

In this paper, we study the MSF algorithm from the perspective of graph structure and investigate the implications of the power-law degree distribution of real-world graphs
on this algorithm.

We introduce the MASTIFF algorithm as a structure-aware MSF algorithm that optimizes work efficiency by (1) dynamically tracking the largest forest component of each graph component and exempting them from processing, and (2) by avoiding topology-related operations such as relabeling and merging neighbour lists.

The evaluations on 2 different processor architectures with up to 128 cores and on graphs of up to 124 billion edges, shows that Mastiff is 3.4–5.9× faster than previous works.

Code Availability
The source-code will be published soon.

BibTex

@INPROCEEDINGS{10.1145/3524059.3532365,
author = {Koohi Esfahani, Mohsen and Kilpatrick, Peter and Vandierendonck, Hans},
title = {{MASTIFF}: Structure-Aware Minimum Spanning Tree/Forest},
year = {2022},
isbn = {},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3524059.3532365},
doi = {10.1145/3524059.3532365},
booktitle = {Proceedings of the 36th ACM International Conference on Supercomputing},
numpages = {13}
}

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SAPCo Sort: Optimizing Degree-Ordering for Power-Law Graphs – ISPASS’22 (Poster)

2022 IEEE International Symposium on Performance Analysis of Systems and Software (ISPASS 2022)
May 22-24, 2022

DOI: 10.1109/ISPASS55109.2022.00015

Authors’ Copy (PDF)

While counting sort has a better complexity than comparison-based sorting algorithms, its parallelization suffers from high performance overhead and/or has a memory complexity that depends on the numbers of threads and vertices.

In this paper, we explore the optimization of parallel counting sort for degree-ordering of real-world graphs with power-law degree distribution and we introduce the Structure-Aware Parallel Counting (SAPCo) Sort algorithm that leverages the skewed degree distribution to accelerate sorting.

The evaluation for graphs of up to 3.6 billion vertices shows that SAPCo sort is, on average, 1.7-33.5 times faster than state-of-the-art sorting algorithms such as counting sort, radix sort, and sample sort.

Code Availability
The source-code of SAPCo will be published soon.

BibTex

@INPROCEEDINGS{10.1109/ISPASS55109.2022.00015,
  author={Koohi Esfahani, Mohsen and Kilpatrick, Peter and Vandierendonck, Hans},
  booktitle={2022 IEEE International Symposium on Performance Analysis of Systems and Software (ISPASS)}, 
  title={{SAPCo Sort}: Optimizing Degree-Ordering for Power-Law Graphs}, 
  year={2022},
  volume={},
  number={},
  pages={},
  publisher={IEEE Computer Society},
  doi={10.1109/ISPASS55109.2022.00015}
}


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LOTUS: Locality Optimizing Triangle Counting – PPOPP’22

27th ACM SIGPLAN Annual Symposium on Principles and Practice of Parallel Programming (PPoPP 2022)
April 2-6, 2022
Acceptance Rate: 31%

DOI: 10.1145/3503221.3508402

Authors’ Copy (PDF Format)

Triangle Counting (TC) is a basic graph algorithm and is widely used in different fields of science, humanities and technology. The great size of real-world graphs with skewed degree distribution is a prohibiting factor in efficient TC.

In this paper, we study the implications of the power-law degree distribution of graph datasets on memory utilization in TC and we explain how a great percentage of triangles are formed around a small number of vertices with very great degrees (that are called hubs).

Using these novel observations, we present the LOTUS algorithm as a structure-aware and locality optimizing TC that separates counting triangles formed by hub and non-hub edges. Lotus introduces bespoke TC algorithms and data structures for different edges in order to (i) reduce the size of data structures that are target of random memory accesses, (ii) to optimize cache capacity utilization, (iii) to provide better load balance, and (iv) to avoid fruitless searches.

To provide better CPU utilization, we introduce the Squared Edge Tiling algorithm that divides a large task into smaller ones when the size of work for each edge in the neighbour-list depends on the index of that edge.

We evaluate the Lotus algorithm on 3 different processor architectures and for real-world graph datasets with up to 162 billion edges that shows LOTUS provides 2.2-5.5 times speedup in comparison to the previous works.

  • LOTUS: Locality Optimizing Triangle Counting
  • LOTUS: Locality Optimizing Triangle Counting
  • LOTUS: Locality Optimizing Triangle Counting - Forward Algorithm
  • LOTUS: Locality Optimizing Triangle Counting - Analysis of Forward Algorithm
  • LOTUS: Locality Optimizing Triangle Counting - Analysis of Forward Algorithm
  • LOTUS: Locality Optimizing Triangle Counting - Analysis of Forward Algorithm
  • LOTUS: Locality Optimizing Triangle Counting - Analysis of Forward Algorithm
  • LOTUS: Locality Optimizing Triangle Counting - Lotus Graph Structure
  • LOTUS: Locality Optimizing Triangle Counting -
  • LOTUS: Locality Optimizing Triangle Counting - HHH & HHN
  • LOTUS: Locality Optimizing Triangle Counting - HNN
  • LOTUS: Locality Optimizing Triangle Counting - NNN
  • LOTUS: Locality Optimizing Triangle Counting - Evaluation
  • LOTUS: Locality Optimizing Triangle Counting - Conclusion
  • LOTUS: Locality Optimizing Triangle Counting -
  • LOTUS: Locality Optimizing Triangle Counting -

Code Availability
The source-code will be published soon.

BibTex

@INPROCEEDINGS{10.1145/3503221.3508402,
  author = {Koohi Esfahani, Mohsen and Kilpatrick, Peter and Vandierendonck, Hans},
  booktitle = {27th ACM SIGPLAN Annual Symposium on Principles and Practice of Parallel Programming (PPoPP 2022)},  
  title = {LOTUS: Locality Optimizing Triangle Counting}, 
  year = {2022},
  numpages = {15},
  pages={219–233},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  doi = {10.1145/3503221.3508402}
}

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Locality Analysis of Graph Reordering Algorithms – IISWC’21

2021 IEEE International Symposium on Workload Characterization (IISWC’21)
November 7-9, 2021
Acceptance Rate: 39.5%
DOI: 10.1109/IISWC53511.2021.00020

Authors’ Copy (PDF Format)

Graph reordering algorithms try to improve locality of graph algorithms by assigning new IDs to vertices that ultimately changes the order of random memory accesses. While graph relabeling algorithms such as SlashBurn, GOrder, and Rabbit-Order provide better locality, it is not clear how they affect graph processing and different graph datasets , mainly, for three reasons:
(1) The large size of datasets,
(2) The lack of suitable measurement tools, and
(3) Disparate characteristics of graphs.
The paucity of analysis has also inhibited the design of more efficient RAs.

This paper introduces a number of metrics and tools to investigate the functionality of graph reordering algorithms and their effects on different real-world graph datasets:
(1) We introduce the Cache Miss Rate Degree Distribution and Degree Distribution of Neighbour to Neighbour Average Distance ID (N2N AID) to show how reordering algorithms affect different vertices,
(2) We introduce the Effective Cache Size as a metric to measure how much of cache capacity is used by reordered graphs for satisfying random memory accesses,
(3) We introduce the Assymetricity Degree Distribution and Neighbourhood Decomposition to explain the composition of neighbourhood of vertices to explain structural differences between web graphs and social networks.
(4) We investigate the effects of the structure of real-world graphs on the locality and performance of traversing graphs in pull and push directions by introducing Push Locality and Pull Locality.

Finally, we present improvements to graph reordering algorithms and propose other suggestions based on the new insights and features of real-world graphs introduced by this paper.

BibTex

@INPROCEEDINGS{10.1109/IISWC53511.2021.00020,
  author={Koohi Esfahani, Mohsen and Kilpatrick, Peter and Vandierendonck, Hans},
  booktitle={2021 IEEE International Symposium on Workload Characterization (IISWC'21)},  
  title={Locality Analysis of Graph Reordering Algorithms}, 
  year={2021},
  volume={},
  number={},
  pages={101-112},
  publisher={IEEE Computer Society},
  doi={10.1109/IISWC53511.2021.00020}
}

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Thrifty Label Propagation: Fast Connected Components for Skewed-Degree Graphs – IEEE CLUSTER’21

IEEE CLUSTER 2021

IEEE CLUSTER 2021
7-10 September

Acceptance rate: 29.4%

DOI: 10.1109/Cluster48925.2021.00042
IEEE Xplore
PDF Version (Authors’ Copy)

Thrifty introduces four optimization techniques to Label Propagation Connected Components:

1) Unified Labels Array accelerates label propagation by allowing the latest label of each vertex to be read in processing other vertices.

2) Zero Convergence optimizes work-efficiency in the pull iterations of Label Propagation by skipping converged vertices.

3) Zero Planting selects the best start propagating point and increases the convergence rate and removes pull iterations that are required for the lowest label to reach the core of graph.

4) Initial Push technique makes the first iteration work efficient by skipping processing edges of vertices that probability of convergence is very small.

Based on these optimizations, Thrifty provides 1.4✕ speedup to Afforest, 6.6✕ to Jayanti-Tarjan, 14.3✕ to BFS-CC, and 25.0✕ to Direction Optimizing Label Propagation.

  • Thrifty Label Propagation: Fast Connected Components For Skewed Degree Graphs
  • Thrifty Label Propagation: Outline
  • Thrifty Label Propagation: Background
  • Thrifty Label Propagation: Background
  • Thrifty Label Propagation: Background
  • Thrifty Label Propagation
  • Thrifty Label Propagation: Unified Labels Array
  • Thrifty Label Propagation: Unified Labels Array
  • Thrifty Label Propagation: Zero Convergence
  • Thrifty Label Propagation: Zero Convergence
  • Thrifty Label Propagation: Zero Planting
  • Thrifty Label Propagation: Zero Planting
  • Thrifty Label Propagation:  Initial Push
  • Thrifty Label Propagation:  Evaluation
  • Thrifty Label Propagation:  Evaluation
  • Thrifty Label Propagation:  Evaluation
  • Thrifty Label Propagation:  Conclusion
  • Thrifty Label Propagation:  Thanks
  • Thrifty Label Propagation:  A Gift from QUB


Code Availability
The source-code will be published soon.


Bibtex

@INPROCEEDINGS{10.1109/Cluster48925.2021.00042,
  author={Koohi Esfahani, Mohsen and Kilpatrick, Peter and Vandierendonck, Hans},
  booktitle={2021 IEEE International Conference on Cluster Computing (CLUSTER)}, 
  title={Thrifty Label Propagation: Fast Connected Components for Skewed-Degree Graphs}, 
  year={2021},
  volume={},
  number={},
  pages={226-237},
  publisher={IEEE Computer Society},
  doi={10.1109/Cluster48925.2021.00042}
}

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Exploiting in-Hub Temporal Locality in SpMV-based Graph Processing – ICPP’21

ICPP'21

50th International Conference on Parallel Processing (ICPP’21)
August 9-12, 2021

Acceptance Rate: 26.4%

DOI:10.1145/3472456.3472462
ACM Digital Library
PDF Version (Authors’ Copy)

This paper investigates the implications made by the structure of real-world graphs with power-law degree distribution on the locality of SpMV graph analytics, and by considering the efficacy of locality optimizing graph reordering algorithms (such as SlashBurn, GOrder, and Rabbit-Order) shows that irregular datasets requires special traversals in order to improve locality for hub vertices that dedicate a large portion of the processing time to themselves.

We introduce in-Hub Temporal Locality (iHTL) as a structure-aware and cache-friendly graph traversal that optimizes locality in pull traversal. iHTL identifies different blocks in the adjacency matrix of a graph and applies a suitable traversal direction (push or pull) for each block based on its contents. In other words, iHTL optimizes locality of one traversal of all edges of the graph by:

(1) applying push direction for flipped blocks containing edges to in-hubs, and
(2) applying pull direction for processing sparse block containing edges to non-hubs.

Moreover, iHTL introduces a new algorithm to efficiently identify the number of flipped blocks by investigating connection between hub vertices of the graph. This allows iHTL to create flipped blocks as much as the graph structure requires and makes iHTL suitable for a wide range of different real-world graph datasets like social networks and web graphs.

iHTL is 1.5× – 2.4× faster than pull and 4.8× – 9.5× faster than push in state-of-the-art graph processing frameworks. More importantly, iHTL is 1.3× – 1.5× faster than pull traversal of state-of-the-art locality optimizing reordering algorithms such as SlashBurn, GOrder, and Rabbit-Order while reduces the preprocessing time by 780×, on average.

  • Exploiting in-Hub Temporal Locality in SpMV-based Graph Processing
  • Exploiting in-Hub Temporal Locality in SpMV-based Graph Processing : Outline
  • Exploiting in-Hub Temporal Locality in SpMV-based Graph Processing : Introduction
  • Exploiting in-Hub Temporal Locality in SpMV-based Graph Processing : Pull vs Push
  • Exploiting in-Hub Temporal Locality in SpMV-based Graph Processing : Is Pull A Suitable Direction
  • Exploiting in-Hub Temporal Locality in SpMV-based Graph Processing : iHTL: in-Hub Temporal Locality
  • Exploiting in-Hub Temporal Locality in SpMV-based Graph Processing : iHTL Graph Structure
  • Exploiting in-Hub Temporal Locality in SpMV-based Graph Processing : SpMV in iHTL
  • Exploiting in-Hub Temporal Locality in SpMV-based Graph Processing : Evaluation
  • Exploiting in-Hub Temporal Locality in SpMV-based Graph : Conclusion
  • Exploiting in-Hub Temporal Locality in SpMV-based Graph : Thanks
  • Exploiting in-Hub Temporal Locality in SpMV-based Graph : A Gift From QUB

Code Availability
The source-code will be published soon.

BibTex


@INPROCEEDINGS{10.1145/3472456.3472462,
author = {Koohi Esfahani, Mohsen and Kilpatrick, Peter and Vandierendonck, Hans},
title = {Exploiting In-Hub Temporal Locality In SpMV-Based Graph Processing},
year = {2021},
isbn = {9781450390682},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3472456.3472462},
doi = {10.1145/3472456.3472462},
booktitle = {50th International Conference on Parallel Processing},
numpages = {10},
location = {Lemont, IL, USA},
series = {ICPP 2021}
}

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How Do Graph Relabeling Algorithms Improve Memory Locality? ISPASS’21 (Poster)

ispass2021-how-do-relaebling-algorithms-improve-memory-locality

IEEE Xplore (DOI: 10.1109/ISPASS51385.2021.00023)
ISPASS-2021
2021 IEEE International Symposium on Performance Analysis of Systems and Software
March 28-30, 2021

Authors’ Copy (PDF Format)

For the complete version of this article, please refer to Locality Analysis of Graph Reordering Algorithms.

Relabeling (reordering) algorithms aim to improve the poor memory locality of graph processing by changing the order of vertices. This paper analyses the functionality of three state-of-the-art relabeling algorithms: SlashBurn, GOrder, and Rabbit-Order for real-world graphs.

We use a number of techniques to explain how locality is affected by relabeling algorithms and how locality of different datasets (like social networks and web graphs) is enhanced by relabeling algorithms.

We use last level cache simulation to study miss rate degree distribution. We also use the degree distribution of Giant Connected Component (GCC) in SlashBurn iterations to see if real-world graphs follow the assumption that “power-law graphs are created/destroyed recursively” [SlashBurn]. We represent SlashBurn++ as an enhanced version of SlashBurn with lower preprocessing time and better locality.

Using cache simulation, we count the number of misses for accessing vertices data of high-degree vertices. This helps to explain how GOrder provides better temporal locality by managing cache space. Average ID Distance (AID) is a spatial locality metric introduced in this paper to explain how clustering relabeling algorithms like Rabbit-Order provide better spatial locality.

This paper also investigates why push and pull traversals of different datasets show different performances by introducing Push Locality and Pull Locality.

Code Availability
The LaganLighter source-code will be published soon.

BibTex

@INPROCEEDINGS{10.1109/ISPASS51385.2021.00023,
  author={Koohi Esfahani, Mohsen and Kilpatrick, Peter and Vandierendonck, Hans},
  booktitle={2021 IEEE International Symposium on Performance Analysis of Systems and Software (ISPASS)}, 
  title={How Do Graph Relabeling Algorithms Improve Memory Locality?}, 
  year={2021},
  volume={},
  number={},
  pages={84-86},
  publisher={IEEE Computer Society},
  doi={10.1109/ISPASS51385.2021.00023}
}

ISPASS’21
ISPASS’21 Final Program
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