LPMetis: Scalable Graph Partitioning for GNNs

• LPMetis is a graph partitioning algorithm that combines label propagation and METIS to create balanced, fast-to-compute partitions for large-scale GNN applications.
• It utilizes a multi-level label propagation framework to compress graphs quickly while preserving structure and ensuring low edge-cuts for effective GNN message passing.
• Empirical evaluations show LPMetis achieves competitive improvements in runtime, partition quality, and downstream GNN performance even on graphs with billions of edges.

Searching arXiv for LPMetis and related large-scale GNN partitioning work. LPMetis, short for Label Propagation with Metis, is a graph partitioning algorithm introduced as the partitioning component of the LPS-GNN framework for deploying graph neural networks on extremely large graphs. It is formulated as a distributed and parallel heuristic and a multi-level framework that uses Multi-Level Label Propagation to quickly compress or coarsen a graph, applies METIS on the final coarsened graph to obtain balanced partitions, and maps those partitions back to the original vertices. Its stated purpose is to make GNN training and inference feasible on super-large graphs, including experiments on graphs with up to 114B edges, by producing partitions that are fast to compute, reasonably balanced in size, sufficiently low-cut to preserve useful structure, and more aligned with message passing than standard partitioners (Cheng et al., 19 Jul 2025).

1. Problem setting and motivation

LPMetis is defined for a graph

$G=(V,E),$

with $N=|V|$ vertices, $|E|$ edges, adjacency matrix $A \in \mathbb{R}^{N\times N}$, and features $X \in \mathbb{R}^{N\times F}$. The graph is partitioned into $K$ disjoint subgraphs,

$P(G)=\{g_1,g_2,\ldots,g_K\},$

which are then used for GNN training and inference.

The motivating problem is that scalable GNN systems on ultra-large graphs remain highly sensitive to the partitioning stage. The target deployment regime includes graphs with 100+ billion edges, and the partitioner must support single-GPU execution while maintaining usable structural fidelity and load balance. In this regime, the paper identifies several limitations in existing partitioning families. Spectral, flow, and recursive bisection methods are described as often too expensive for huge graphs, dependent on global graph information, and difficult to keep balanced while maintaining low cut. METIS is characterized as strong on smaller graphs but insufficiently scalable for the largest graphs considered. ParMETIS, RGP, and other scalable variants can scale further than METIS, but are presented as still inadequate for the largest settings in the study or as less efficient or less robust across graph distributions. Pure community detection or LPA-based methods are fast and scalable, but do not guarantee balanced partitions, can oscillate in bipartite or dichotomous settings, and may form giant communities that degrade GNN batching and load balance (Cheng et al., 19 Jul 2025).

This framing places LPMetis in a distinct design space. Its objective is not only graph-theoretic edge-cut minimization, but partition construction that is explicitly compatible with GNN message passing and mini-batch execution.

2. Position within LPS-GNN

Within LPS-GNN, LPMetis is the first of three main components: partitioning using LPMetis, subgraph augmentation, and GNN training/inference. The partitioner is therefore not an isolated preprocessing utility; it determines the computational units on which all later stages operate.

The workflow described for Partition-based Billion-scale Graph Neural Networks (LPS-GNN) is:

1. Partition graph $G$ into $K$ subgraphs $g_1,\dots,g_K$ by LPMetis.
2. Build a global coarsened graph $N=|V|$0 from those partitions using edge-based coarsening.
3. Compute global embeddings on the coarsened graph using an unsupervised GNN, with DGI given as the default example.
4. Repeatedly sample a subgraph $N=|V|$1.
5. Augment its node features with global embeddings:

$N=|V|$2

1. Refine the subgraph structure via structural augmentation.
2. Train a supervised GNN on the augmented subgraph batch.
3. Repeat until convergence.

In this formulation, LPMetis provides the decomposition that makes subsequent coarsened-graph embedding, feature augmentation, structure refinement, and supervised training computationally tractable. A plausible implication is that partition quality affects not only runtime and memory, but also the quality of the global embeddings and the efficacy of the later augmentation stages (Cheng et al., 19 Jul 2025).

3. Algorithmic structure

LPMetis is described as combining LPA’s speed and propagation-based grouping with METIS’s partition balance quality. The method differs from standard METIS-style multilevel partitioning in that it uses different operators at different levels, rather than repeatedly applying the same coarsening strategy.

The algorithmic workflow is given as follows.

First, initialize the working graph: $N=|V|$3

Then, for $N=|V|$4 to $N=|V|$5:

• run MultiLevelLP(\tilde{G}, T) to obtain communities or subgraphs $N=|V|$6;
• coarsen the graph by edge-based coarsening:

$N=|V|$7

After the loop, the method performs one additional node-based coarsening: $N=|V|$8

Finally, it runs METIS on the last coarsened graph: $N=|V|$9 then maps the subgraph identifiers back to the original vertices of $|E|$0.

The distinction between the two coarsening modes is explicit. In coarsening by edge, the node value of a coarsened node is the number of nodes in the subgraph from the previous coarsened graph, which is described as suitable for preserving structure as a compressed representation. In coarsening by node, the value of a coarsened node is the total number of original nodes it represents, which is described as suitable for obtaining a final balanced representation. During coarsening, inter-partition edge weights are accumulated according to

$|E|$1

for edges $|E|$2 whose endpoints fall into coarsened subgraphs $|E|$3 and $|E|$4 (Cheng et al., 19 Jul 2025).

The final METIS stage is the balancing mechanism in the overall design. The preceding label-propagation and coarsening stages reduce the problem size rapidly, after which METIS is applied on a much smaller graph.

4. Multi-Level Label Propagation

The central subroutine inside LPMetis is Multi-Level LP, which serves as the fast segmentation engine during graph compression. The procedure initializes each node with its own label,

$|E|$5

then repeats a weighted label-propagation process for $|E|$6 iterations. At each iteration, a node updates its label to the highest-frequency label among its neighbors, weighted by edge importance; labels are propagated through edges; and edges whose computed importance becomes $|E|$7 are deleted. Nodes are then grouped by final labels into clusters $|E|$8.

This mechanism is introduced as a response to known failure modes of plain LPA. The paper states that standard LPA can oscillate, fail to converge in bipartite graphs, ignore edge weights, and produce poor partitions for GNNs. LPMetis addresses these issues by incorporating edge weights, node values, and progressive coarsening.

A key design element is a weighted edge-retention rule in which $|E|$9 is determined from the relative importance of edge $A \in \mathbb{R}^{N\times N}$0 among the neighbors of $A \in \mathbb{R}^{N\times N}$1. If an edge is strong enough, it is kept; otherwise it may still be retained randomly with probability threshold $A \in \mathbb{R}^{N\times N}$2. For unweighted graphs, the edge weight is $A \in \mathbb{R}^{N\times N}$3. The paper interprets this as deliberate tolerance of some edge cutting in exchange for speed and balance, on the assumption that very large graphs are sufficiently redundant or noisy that not every edge must be preserved (Cheng et al., 19 Jul 2025).

The weighted label update is likewise not a naive majority vote. The paper gives a weighted aggregation expression in which each neighbor contributes according to the edge weight $A \in \mathbb{R}^{N\times N}$4 and the current “mass” or size $A \in \mathbb{R}^{N\times N}$5 of the coarsened node, after which the label with the largest weighted support is selected. This suggests that LPMetis is designed to avoid the instability of unweighted label propagation on skewed or weighted graph topologies.

5. Evaluation criteria and empirical behavior

LPMetis is evaluated with four partitioning metrics: runtime, Edge-Cut (EC), Balancing (BAL), and Standard Deviation (STD). The paper defines

$A \in \mathbb{R}^{N\times N}$6

$A \in \mathbb{R}^{N\times N}$7

where MaxLoad is the number of edges in the most loaded partition, and

$A \in \mathbb{R}^{N\times N}$8

Lower values are preferred for EC, BAL, and STD. For downstream GNN quality, the paper reports AUC, Precision, Recall, and F1.

On ogbn-products, LPMetis is compared with METIS inside Cluster-GCN variants. The paper reports Cluster-GCN (METIS) test accuracy 0.74553 and Cluster-GCN (LPMetis) test accuracy 0.75272, with similar gains for GAT and SAGE variants. This is presented as evidence that LPMetis remains competitive even on smaller public benchmarks where METIS is already strong (Cheng et al., 19 Jul 2025).

On the billion-scale dataset $A \in \mathbb{R}^{N\times N}$9, the paper compares LPMetis against LPA, FF, FFD, and RGP. The reported results are:

Method	Precision	Recall / F1
LPS-GNN (RGP)	75.29%	Recall 75.68%, F1 75.44%
LPS-GNN (LPMetis)	76.03%	Recall 76.10%, F1 76.06%

The reported gain is about 0.55%–0.98% depending on metric. The accompanying explanation is that FFD creates too many small subgraphs, FF and LPA can generate excessively large subgraphs, and LPMetis preserves more useful edges while still producing GNN-compatible partitions.

Across multiple graph partition benchmarks, the qualitative pattern reported is that METIS is strong on smaller graphs but can hit OOM on larger ones, LPA is fast but unstable and imbalanced, RGP is balanced but slower or less efficient, and LPMetis occupies a strong middle ground. The paper further notes that RGP can become ineffective because its edge-cut becomes so extreme that BAL and STD lose meaning, whereas LPMetis remains robust across graph scales and graph distributions (Cheng et al., 19 Jul 2025).

6. Scalability, downstream effects, and nomenclature

LPMetis is part of the system-level argument for running large-graph GNN workloads with substantially reduced infrastructure. The paper compares Angel Graph training, which uses 10 PS workers + 70 Spark executors and about 2160 GB memory, with LPS-GNN, which uses a single GPU and 60 executors, with about 15% lower memory usage in the reported setup. On dataset $X \in \mathbb{R}^{N\times F}$0, preprocessing time is reported as 178 min for Angel GraphSAGE preprocessing and 145 min for LPS-GNN (GCN), corresponding to an 18.53% reduction. LPMetis is claimed to have overall time complexity

$X \in \mathbb{R}^{N\times F}$1

because Multi-Level LP is near-linear and converges in only 2–3 iterations in practice (Cheng et al., 19 Jul 2025).

The effect extends to downstream learning. On offline $X \in \mathbb{R}^{N\times F}$2, the paper reports LPS-GNN (GraphMAE) with AUC 0.875 and LPS-GNN (GCN) with AUC 0.833, both outperforming Angel Graph baselines. A sampling ablation over LPMetis-produced subgraphs reports all subgraphs: 16h, F1 = 0.7693, 10%: 7h, F1 = 0.8183, and 5%: 3h, F1 = 0.8269. The paper also reports that the best result in the subgraph augmentation ablation is SR-PR + FA with Precision 0.8925, Recall 0.8199, and F1 0.8547. This suggests that LPMetis is not only a partitioning accelerator but also part of a partition–augmentation pipeline in which subgraph quality affects predictive performance.

A recurrent source of confusion is nomenclature. Despite the surface similarity between LPMetis and LPM, they refer to unrelated methods. LPMetis is a graph partitioning heuristic for large-scale GNN deployment (Cheng et al., 19 Jul 2025). By contrast, the Local Pivotal Method (LPM) is a balanced sampling method originally designed for discrete populations and extended as a general variance reduction approach for continuous distributions, where it creates “automatic stratification” and a thin, well-spread sample (Olofsson et al., 2023). The overlap is therefore lexical rather than methodological.