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Fast UMAP-Based Graph Drawing

Authors Amyra Meidiana , Seok-Hee Hong

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ACM Subject Classification
  • Human-centered computing → Graph drawings
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Graph algorithms
Keywords
  • Graph Drawing
  • UMAP
  • Spectral Sparsification

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Abstract

We present three fast UMAP-based graph drawing algorithms that reduce the time complexity of naive GUMAP from O(nm) to O(n² log n) and to O(n). Specifically, we reduce the time complexity for three components: (C0) O(nm)-time computation of all-pairs shortest paths, (C1) O(n² log n)-time computation of the kNN, and (C2) O(n)-time optimization of the cost function.
First, we present O(n² log n)-time SS-GUMAP, which utilizes spectral sparsification to compute a subgraph G' preserving structural properties of a graph G. Next, we present O(n)-time SL-GUMAP, which utilizes O(n)-time partial BFS to compute the shortest paths and kNN for C0 and C1, and sublinear-time O(n^0.9) edge sampling to reduce the cost optimization iterations for C2. Finally, we present a faster O(n)-time SSSL-GUMAP combining both approaches (i.e., running SL-GUMAP on the spectral sparsification G' of G) to reduce C0 and C1 to O(n) time and C2 to sublinear time, with faster runtime than SL-GUMAP in execution. Extensive experiments demonstrate that SS-GUMAP runs 28% faster than the baseline GUMAP, and SL-GUMAP and SSSL-GUMAP run 80% and 83% faster, respectively, while maintaining similar quality metrics and visual quality.

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Amyra Meidiana and Seok-Hee Hong. Fast UMAP-Based Graph Drawing. In 34th International Symposium on Graph Drawing and Network Visualization (GD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 396, pp. 30:1-30:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.GD.2026.30

Author Details

Amyra Meidiana
  • The University of Sydney, Australia
Seok-Hee Hong
  • The University of Sydney, Australia

Funding

ARC (Australian Research Council) DP (Discovery Project) grant

References

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