GrAlgoBench: Graph Algorithm Benchmark Suite

• GrAlgoBench is a domain-specific benchmarking suite designed to rigorously evaluate graph algorithms on modern architectures with realistic graph generation and representative kernel workloads.
• It employs a parallel, Barabási–Albert-based graph generator to produce scale-free synthetic graphs that mirror real-world structural properties.
• The suite includes five kernels covering search, spectral, structural, and optimization tasks, enabling reproducible and architecture-neutral performance comparisons.

GrAlgoBench is a domain-specific benchmarking suite for the rigorous evaluation of graph-theoretic algorithms on modern computational architectures. Designed to address methodological and implementation gaps in existing evaluation tools, GrAlgoBench provides a synthetic, scale-free graph generator, a suite of five representative computational kernels—encompassing search, spectral, structural, metric, and global optimization workloads—and precise complexity models and pseudocode, all within a reproducible and architecture-neutral protocol. By modeling realistic algorithmic and memory-access patterns, GrAlgoBench enables systematized comparison of platforms, data layouts, and programming models for diverse graph problems (Yoo et al., 2010).

1. Design Motivations and Benchmark Objectives

The primary motivation for GrAlgoBench is the detailed and fair evaluation of graph algorithm performance, particularly under the constraints typical of real-world, large-scale graph analytics. Classical application contexts, including web mining, social network analysis, and bioinformatics, demand scalable, low-overhead measurements of both computation and memory system efficacy. GrAlgoBench was developed in response to distinct deficiencies in earlier suites such as SSCA#2, including limited algorithmic diversity, oversimplified or unrealistic graph generators (notably R-MAT), and evaluation kernels whose exactness and memory characteristics deviate from those of widely studied algorithms.

Design priorities are:

• Comprehensiveness: Inclusion of five kernels representative of fundamental graph problem classes: single-source shortest paths (search), spectral eigenvector computation, adjacency-centric vertex/edge manipulations, local clustering metrics, and global, community-centric optimizations.
• Faithful Modeling: Retention of algorithmic and memory-access signatures true to their theoretical and practical implementations, eschewing shortcuts (e.g., nonstandard betweenness approximations) that might distort architectural comparisons.
• Reproducibility and Tractability: Fixing graph formats (adjacency list and CSR), pseudorandom initialization, and unimposing kernel computational costs to allow scalable evaluation even on graphs with |V|,|E| ≫ 10⁶.

2. Graph Generation Methodology

At the core of GrAlgoBench is a parallel, preferential-attachment generator implementing the Barabási–Albert model. This method constructs sparse, power-law (scale-free) graphs by probabilistically favoring existing high-degree nodes during edge creation. The procedure initializes with a clique of size c; subsequently, each new node samples its degree and attaches to previously added nodes, with edge selection proportional to current degree, guaranteeing O(m) generation time (where m=|E|). The generator outputs undirected weighted graphs, with edge weights and node color attributes drawn uniformly from [0,1]. This synthetic paradigm mirrors key structural properties—such as heavy-tailed degree distribution and local clustering—observed in empirical networks, supporting realistic kernel behavior (Yoo et al., 2010).

3. Computational Kernels

GrAlgoBench defines five distinct kernels, each articulated with formal problem descriptions, pseudocode, and established complexity bounds:

Kernel	Problem Class	Core Operation
1	Graph Search	SSSP (generalized BFS/Dijkstra)
2	Spectral Analysis	Power-method eigenvector computation
3	Vertex/Edge Accesses	Hierarchicalization via super-node merges
4	Graph Metric	Clustering coefficient computation
5	Global Optimization	Entropy-based community detection

Kernel 1 employs a priority-queue-based SSSP, supporting both classic Dijkstra (O((|V|+|E|)log|V|)) and bucket-based variants for integer weights (O(|V|+|E|)). Kernel 2 uses the power method to approximate the dominant eigenvector of the adjacency matrix, iterating until convergence or a maximum threshold, with per-iteration cost linear in the number of edges. Kernel 3 performs repeated coalescences, randomly merging a node and its neighborhood into a super-node, exercising both adjacency accesses and dynamic structural updates. Kernel 4 computes local clustering coefficients for a random sample of nodes, explicitly enumerating two-hop adjacency relationships. Kernel 5 implements a greedy split-based, entropy-maximizing community detection procedure, iteratively partitioning the vertex set according to a density-based objective using binary entropy H(p).

All kernels are defined for both adjacency list and CSR (compressed-sparse row) storage, ensuring robustness of evaluation against memory-layout effects.

4. Dataset Construction and Kernel Execution

The synthetic graphs produced by GrAlgoBench’s generator serve as the exclusive input for all kernel executions. Graph size (|V|), average degree (D), clique seed (c), and internal randomization seeds are specified to produce reproducible benchmark instances. Both memory layouts (adjacency-list and CSR) are used side-by-side, allowing empirical bounding of memory-system stress.

In executing the kernels, users are instructed to:

• Fix key control parameters (e.g., convergence ε for the power method, reduction ratio r in hierarchicalization) to isolate hardware or software effects.
• Maintain consistent graph instances across all kernels and platforms for valid comparison.
• Report wall-clock runtime, memory footprint, and, when possible, bandwidth or energy metrics.
• Present all results together to reveal system-level behaviors relevant to real analytic workloads, such as pointer chasing, irregular linear algebra, and neighborhood-centric memory traversals.

5. Complexity Analysis and Theoretical Models

Each kernel is described with precise asymptotic complexity:

• Graph generator: O(m) work, trivial parallelization.
• Kernel 1: O((|V|+|E|)log|V|) or O(|V|+|E|); optimal for sparse graphs.
• Kernel 2: O(m_max·|E|), where m_max is iteration cap.
• Kernel 3: O(|V|+|E|), dominated by cumulative neighbor adjacency updates.
• Kernel 4: O(∑ deg(u)²) for m-sampled vertices.
• Kernel 5: O(m·|V|·|E|) in the worst case, considering up to m iterations of full clustering evaluation.

Formal equations are provided in the suite for convergence, clustering coefficient, and the community detection entropy objective:

$$\mathrm{CC}(u)=\frac{\bigl|\{(v,v')\in E: v,v'\in\mathrm{Adj}(u)\}\bigr|}{|\mathrm{Adj}(u)|(|\mathrm{Adj}(u)|-1)}$$

$$\mathrm{Obj}(C) = \sum_{g\in C} H(\mathrm{density}(g)), \quad H(p) = -p\log_2p - (1-p)\log_2(1-p)$$

These cost models ensure the benchmark reflects realistic operational intensities and caches contention, crucial for accurate performance evaluation on diverse hardware (Yoo et al., 2010).

6. Application Protocol and Best Practices

Application of GrAlgoBench follows a tightly specified workflow:

1. Select desired graph parameters and generate synthetic graphs once per experimental campaign.
2. Encode each graph in both adjacency-list and CSR formats.
3. Run all five kernels using fixed control parameters, repeatedly if necessary for timing precision.
4. Gather and report evaluation metrics—runtime, space, and bandwidth—across all kernels and layouts.
5. Present comparative data across platforms, architectures, or programming models to elucidate distinctions, especially in managing irregular, data-intensive workloads.

Reporting results for all kernels on the same graph and with controlled parameters is essential to derive meaningful architecture-level observations.

7. Context, Impact, and Extensibility

GrAlgoBench was introduced to fill substantive gaps in prior benchmarking approaches for graph workloads, particularly limitations in scope, fidelity to realistic graph structure, and comparability across platforms. By incorporating an efficient, realistic generator, comprehensive kernel coverage, and explicit complexity and pseudocode, it enables reproducible analyses of CPU/GPU architectures, memory hierarchies, and data storage formats under the demands characteristic of modern, large-scale graph analytics.

While empirical performance results are not provided in the original technical report, all necessary algorithmic detail and experimental guidance are included to allow research teams to implement and extend the suite. This positioning makes GrAlgoBench a foundational resource for architectural evaluation and software performance engineering in graph-theoretic computation (Yoo et al., 2010).