# Parallel Maximum Clique Algorithms with Applications to Network Analysis and Storage

arXiv: https://arxiv.org/abs/1302.6256 · HTML: https://mlsanity.com/paper/1302.6256/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2013.

## Built on by (most cited first, 15 of 15)

- [Kimera-Multi: Robust, Distributed, Dense Metric-Semantic SLAM for Multi-Robot Systems](https://mlsanity.com/paper/2106.14386/) (2021)
- [A Single Correspondence Is Enough: Robust Global Registration to Avoid Degeneracy in Urban Environments](https://mlsanity.com/paper/2203.06612/) (2022)
- [KISS-Matcher: Fast and Robust Point Cloud Registration Revisited](https://mlsanity.com/paper/2409.15615/) (2024)
- [ARCS: Accurate Rotation and Correspondence Search](https://mlsanity.com/paper/2203.14493/) (2022)
- [G3Reg: Pyramid Graph-based Global Registration using Gaussian Ellipsoid Model](https://mlsanity.com/paper/2308.11573/) (2023)
- [Efficient and Robust Point Cloud Registration via Heuristics-guided Parameter Search](https://mlsanity.com/paper/2404.06155/) (2024)
- [Optimal and Robust Category-level Perception: Object Pose and Shape Estimation from 2D and 3D Semantic Keypoints](https://mlsanity.com/paper/2206.12498/) (2022)
- [Pyramid Semantic Graph-based Global Point Cloud Registration with Low Overlap](https://mlsanity.com/paper/2307.12116/) (2023)
- [CLIPPER+: A Fast Maximal Clique Algorithm for Robust Global Registration](https://mlsanity.com/paper/2402.15464/) (2024)
- [HyperGCT: A Dynamic Hyper-GNN-Learned Geometric Constraint for 3D Registration](https://mlsanity.com/paper/2503.02195/) (2025)
- [View-Invariant Localization using Semantic Objects in Changing Environments](https://mlsanity.com/paper/2209.14426/) (2022)
- [QuadricsReg: Large-Scale Point Cloud Registration using Quadric Primitives](https://mlsanity.com/paper/2412.02998/) (2024)
- [A short review on the maximum clique problem algorithms with classical, AI, and quantum methods](https://mlsanity.com/paper/2403.09742/) (2024)
- [Instance-Aware Algorithm Selection for Maximum Clique via a Dual-Channel Graph Neural Architecture](https://mlsanity.com/paper/2508.08005/) (2025)
- [Gaussian Semantic Field for One-shot LiDAR Global Localization](https://mlsanity.com/paper/2510.12101/) (2025)

## Abstract (arXiv)

We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. The method exhibits a roughly linear runtime scaling over real-world networks ranging from 1000 to 100 million nodes. In a test on a social network with 1.8 billion edges, the algorithm finds the largest clique in about 20 minutes. Our method employs a branch and bound strategy with novel and aggressive pruning techniques. For instance, we use the core number of a vertex in combination with a good heuristic clique finder to efficiently remove the vast majority of the search space. In addition, we parallelize the exploration of the search tree. During the search, processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with large search spaces can be pruned by other processes. We apply the algorithm to two problems: to compute temporal strong components and to compress graphs.