[Paper] ESCHER: Efficient and Scalable Hypergraph Evolution Representation with Application to Triad Counting

Source: arXiv - 2512.21009v1

Overview

The paper introduces ESCHER, a GPU‑focused data structure that makes it practical to store, update, and query massive, evolving hypergraphs. By coupling this representation with a clever triad‑counting algorithm, the authors achieve orders‑of‑magnitude speedups on dynamic hypergraph analytics—something that has been largely infeasible with existing graph‑only tools.

Key Contributions

• ESCHER data structure: A memory‑efficient, GPU‑resident representation tailored for dynamic hypergraphs, supporting fast insertions, deletions, and queries.
• Triad‑count update framework: An incremental algorithm that recomputes only the affected triads after a hyperedge change, avoiding full recomputation.
• Comprehensive evaluation: Benchmarks on real‑world (e.g., co‑authorship, email, and social interaction) and synthetic hypergraphs across three triad definitions (hyperedge‑based, incident‑vertex‑based, temporal).
• Performance breakthroughs: Demonstrated speedups of up to 104.5×, 473.7×, and 112.5× over the best prior CPU‑based and GPU‑based baselines for the three triad types.
• Open‑source implementation: The authors release the ESCHER library (CUDA code) and scripts for reproducibility, filling a tooling gap in the hypergraph community.

Methodology

1. Hypergraph model: A hypergraph (H = (V, E)) where each hyperedge (e \in E) can connect any number of vertices. The authors focus on triads—sets of three vertices that co‑occur in at least one hyperedge, with three variants:

   • Hyperedge‑based: three vertices appear together in a single hyperedge.
   • Incident‑vertex‑based: each pair of the three vertices shares at least one hyperedge (not necessarily the same one).
   • Temporal: triads that exist within a sliding time window.

2. ESCHER design:

   • Compressed adjacency lists stored in GPU global memory, using a two‑level index (hyperedge → vertex list) that enables coalesced memory accesses.
   • Bit‑mask signatures per hyperedge to quickly test vertex membership without scanning the full list.
   • Dynamic buffers for batched insert/delete operations, allowing the GPU to amortize kernel launch overhead.

3. Incremental triad counting:

   • When a hyperedge is added/removed, ESCHER identifies the affected vertex subsets via the bit‑mask signatures.
   • Only triads that include at least one vertex from the changed hyperedge are recomputed.
   • Parallel kernels enumerate candidate triples and update a global counter using atomic operations or warp‑level reductions, depending on triad type.

4. Evaluation pipeline: The authors compare ESCHER against:

   • A naïve CPU baseline that recomputes triads from scratch after each update.
   • A prior GPU method that stores hypergraphs as flattened edge‑lists but lacks incremental updates.
   • Various dataset sizes (10⁴–10⁸ vertices, 10⁵–10⁹ hyperedges) and update rates (10³–10⁶ operations per second).

Results & Findings

• Scalability: ESCHER maintains near‑linear throughput as the hypergraph grows, thanks to its batched update strategy and GPU memory layout.
• Memory footprint: The compressed representation uses ~30 % less GPU memory than the flat edge‑list baseline, enabling larger graphs to fit on a single GPU.
• Accuracy: Since the algorithm is exact (not an approximation), the speed gains come purely from reduced work and parallelism.

Practical Implications

• Real‑time analytics: Platforms that monitor collaborative activities (e.g., code repositories, chat rooms, IoT sensor groups) can now maintain up‑to‑date triad statistics with sub‑millisecond latency, enabling anomaly detection or recommendation engines that react instantly to group formation changes.
• Hypergraph‑aware ML pipelines: Feature extraction for hypergraph neural networks often relies on higher‑order motifs; ESCHER makes it feasible to recompute motif counts on the fly during training or inference, improving model freshness without costly offline preprocessing.
• Network science tools: Existing graph libraries (NetworkX, SNAP) can integrate ESCHER as a GPU backend for hypergraph modules, extending their capability to handle dynamic, higher‑order data at scale.
• Cost efficiency: By squeezing more work per GPU and reducing memory usage, organizations can achieve the same analytical throughput with fewer hardware resources, lowering cloud compute bills.

Limitations & Future Work

• GPU memory bound: Extremely massive hypergraphs (beyond ~10⁹ hyperedges) still exceed a single GPU’s memory; multi‑GPU or out‑of‑core extensions are not covered.
• Atomic contention: For very dense updates, atomic increments on the global triad counter can become a bottleneck; alternative reduction schemes could be explored.
• Triad definition scope: The paper focuses on three triad variants; extending the framework to larger motifs (e.g., 4‑vertex hyper‑cliques) or custom user‑defined patterns remains an open challenge.
• Dynamic vertex set: While hyperedge insert/delete is fully supported, adding or removing vertices (and re‑indexing) requires a full rebuild of the ESCHER structure, which the authors note as future work.

Authors

• S. M. Shovan
• Arindam Khanda
• Sanjukta Bhowmick
• Sajal K. Das

Paper Information

• arXiv ID: 2512.21009v1
• Categories: cs.DC, cs.DS
• Published: December 24, 2025
• PDF: Download PDF