Tag Archives: graph relabeling

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

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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 elements.

In this paper, we explore the optimization of parallel counting sort for degree-ordering of real-world graphs with skewed 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.

For a detailed explanation of the algorithms, please refer to Chapter 5 of the On Designing Structure-Aware High-Performance Graph Algorithms thesis.

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}
}

Code Availability
The source-code of SAPCo is available on LaganLighter Repository (alg1_sapco_sort.c and relabel.c files). A sample execution of this source code for “Twitter-MPI” graph is shown in the following:


LaganLighter

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Locality Analysis of Graph Reordering Algorithms – IISWC’21

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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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LaganLighter

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

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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}
}

LaganLighter

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

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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 a complete version of this article, please refer to Locality Analysis of Graph Reordering Algorithms and also Chapter 3 of the On Designing Structure-Aware High-Performance Graph Algorithms thesis.

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.

  • How Do Graph Relabeling Algorithms Improve Memory Locality?
  • Outline
  • What is Locality?
  • What is Graph Relabeling (Reordering) ?
  • Why is Relabeling Important for Graph Processing?
  • Why is Relabeling Important for Graph Processing?
  • Graph Traversals
  • Performance of Relabeling Algorithms
  • Performance of Relabeling Algorithms
  • Performance of Relabeling Algorithms
  • SlashBurn: Community Detection for Power-law Graphs
  • SlashBurn: Community Detection for Power-law Graphs
  • SlashBurn++
  • GOrder: Cache Simulation for Pull Traversal
  • GOrder: Cache Simulation for Pull Traversal
  • Rabbit-Order: Parallel Community Detection
  • Rabbit-Order: Parallel Community Detection
  • Rabbit-Order: Parallel Community Detection
  • Push Locality vs. Pull Locality
  • Push Locality vs. Pull Locality
  • Conclusion
  • Thanks
  • QUB

Code Availability
The source-code of LaganLighter is available on LaganLighter Repository.

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
LaganLighter

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