Parallel Heuristics for Scalable Community Detection (1410.1237v2)

Abstract: Community detection has become a fundamental operation in numerous graph-theoretic applications. It is used to reveal natural divisions that exist within real world networks without imposing prior size or cardinality constraints on the set of communities. Despite its potential for application, there is only limited support for community detection on large-scale parallel computers, largely owing to the irregular and inherently sequential nature of the underlying heuristics. In this paper, we present parallelization heuristics for fast community detection using the Louvain method as the serial template. The Louvain method is an iterative heuristic for modularity optimization. Originally developed by Blondel et al. in 2008, the method has become increasingly popular owing to its ability to detect high modularity community partitions in a fast and memory-efficient manner. However, the method is also inherently sequential, thereby limiting its scalability. Here, we observe certain key properties of this method that present challenges for its parallelization, and consequently propose heuristics that are designed to break the sequential barrier. For evaluation purposes, we implemented our heuristics using OpenMP multithreading, and tested them over real world graphs derived from multiple application domains (e.g., internet, citation, biological). Compared to the serial Louvain implementation, our parallel implementation is able to produce community outputs with a higher modularity for most of the inputs tested, in comparable number or fewer iterations, while providing absolute speedups of up to 16x using 32 threads.

• The paper presents novel parallel heuristics, including the minimum label and coloring strategies, that overcome sequential dependencies in the Louvain method for up to 16x speedup.
• The study applies vertex following preprocessing to condense single-degree vertices, effectively reducing computational overhead and focusing on complex interactions.
• Experimental results across diverse graphs show enhanced modularity and accelerated convergence, although certain datasets revealed prolonged hub interactions.

Parallel Heuristics for Scalable Community Detection

The paper presents a comprehensive paper on parallelization strategies for community detection in large-scale graphs, specifically targeting the Louvain method, which is widely recognized for its modularity optimization prowess. Community detection, an integral operation in graph theory applications, involves identifying intrinsic subdivisions within networks to uncover inherent patterns without predefined constraints. Despite the importance, existing methodologies face limitations in scalability on parallel computing architectures due to the sequential dependencies inherent in heuristic approaches.

Louvain Method and Parallelization Challenges

The Louvain method is a popular iterative algorithm introduced by Blondel et al., primarily focused on modularity optimization to detect community structures. It starts with each vertex in its own community and iteratively optimizes modularity by merging communities based on maximal gain, refining community partitions, and progressively condensing the graph iteratively in phases. However, its inherent sequential nature poses challenges for parallelization, as community updates based on vertices often rely on previously optimized values, potentially leading to inconsistent states if performed independently across processors.

Key complexities in parallelizing the Louvain method arise from scenarios like negative gains and swap/local maxima, where concurrent updates can cause suboptimal convergence and potential algorithmic stagnation. For example, two vertices might independently decide to join the same neighboring community, but their concurrent moves could collectively result in lower modularity due to mutual exclusivity or inadequate accounting of interactions, thereby reducing process effectiveness and convergence certainty.

Proposed Parallel Heuristics

To address these challenges, the authors propose several heuristics that improve parallel performance without compromising output quality:

1. Minimum Label Heuristic: This heuristic curtails vertex swapping by enforcing hierarchical merging based on pre-assigned community labels. By restricting movements to communities with lesser labels during competitive decision scenarios, the algorithm circumvents unnecessary swaps and facilitates quicker convergence.
2. Coloring Strategy: Utilizes graph coloring to facilitate non-conflicting parallel execution, allowing vertices of the same color to be processed independently while ensuring distanced vertices avoid concurrent updates. Though not guaranteeing complete exclusion of negative gains scenarios, it effectively reduces the occurrences and improves modularity results.
3. Vertex Following Heuristic: Predicated on graph preprocessing, it condenses single-degree vertices into their neighbors before processing, reducing overhead and focusing computational efforts on complex interactions. This approach abstracts minor influences, emphasizing connective hubs.

Experimental Evaluation and Results

Experiments were conducted across a diverse set of graphs to validate the proposed heuristics. The implementation using OpenMP achieved notable speedups of up to 16x compared to the serial Louvain method, especially evident in networks with high modularity structures. While comparisons showed an increase in modularity in several datasets, a unique result was observed in Europe-osm and Rgg_n_2_24_s0, where vertex following preprocessing prolonged convergence due to extended hub interactions. Coloring heuristics displayed benefits by reducing the number of iterations, critical in accelerating solution time. The modularity gain threshold was explored, favoring a higher value with faster convergence and negligible loss in modularity quality.

Implications and Future Directions

The heuristics proposed offer practical improvements to the scalability of community detection algorithms, which are critical as graph datasets continue to grow exponentially. By enriching parallel architectures with optimized strategies, the paper contributes significantly to the computational efficacy of the Louvain method, rendering it feasible for real-time and increasingly dense graphs.

Future work involves extending heuristics to encompass resolution-limited modularity optimizations, assessing community structure stability across parallel implementations, and further refining coloring methods for balanced graph segmentation. The authors recognize the need for enhanced graph rebuilding mechanisms between phases and aim to investigate distributed memory frameworks for broader application scope.

In summary, the paper provides a detailed account of effective strategies to parallelize community detection, specifically by augmenting the Louvain method for scalable graph analysis, while assessing key performance and output quality facets through rigorous experimental validation. The insights establish a foundational reference for advancing computational graph theory paradigms within parallel computing environments.