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Sublinear Spectral Clustering Oracle with Little Memory

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Graph ClusteringSpectral ClusteringMemory-Efficient AlgorithmsSublinear AlgorithmsSpace-Time Trade-offs
Abstract:

We study the problem of designing sublinear spectral clustering oracles for well-clusterable graphs. Such an oracle is an algorithm that, given query access to the adjacency list of a graph GG, first constructs a compact data structure D\mathcal{D} that captures the clustering structure of GG. Once built, D\mathcal{D} enables sublinear time responses to \textsc{WhichCluster}(G,x)(G,x) queries for any vertex xx. A major limitation of existing oracles is that constructing D\mathcal{D} requires Ω(n)\Omega(\sqrt{n}) memory, which becomes a bottleneck for massive graphs and memory-limited settings. In this paper, we break this barrier and establish a memory-time trade-off for sublinear spectral clustering oracles. Specifically, for well-clusterable graphs, we present oracles that construct D\mathcal{D} using much smaller than O(n)O(\sqrt{n}) memory (e.g., O(n0.01)O(n^{0.01})) while still answering membership queries in sublinear time. We also characterize the trade-off frontier between memory usage SS and query time TT, showing, for example, that S⋅T=O~(n)S\cdot T=\widetilde{O}(n) for clusterable graphs with a logarithmic conductance gap, and we show that this trade-off is nearly optimal (up to logarithmic factors) for a natural class of approaches. Finally, to complement our theory, we validate the performance of our oracles through experiments on synthetic networks.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces sublinear spectral clustering oracles that break the Ω(√n) memory barrier, achieving memory usage as low as O(n^0.01) while maintaining sublinear query time. Within the taxonomy, it resides in the 'Memory-Time Trade-off Oracles' leaf under 'Sublinear-Time Clustering Oracles'. This leaf contains only two papers total, indicating a relatively sparse research direction. The sibling paper in this leaf shares the focus on explicit memory-time trade-offs, suggesting this is an emerging rather than crowded area of investigation.

The taxonomy reveals that the broader 'Sublinear-Time Clustering Oracles' branch contains a 'Standard Sublinear Oracles' leaf with papers accepting O(√n) or higher memory usage. Neighboring branches include 'Sequential and Streaming Approaches' (processing data incrementally) and 'Memory-Efficient Batch Methods' (using sampling or decomposition). The paper's oracle-based query model distinguishes it from streaming methods that process continuous arrivals, and from batch methods that require full dataset access. Its focus on preprocessing into compact structures for repeated queries positions it between pure streaming and traditional batch paradigms.

Among 24 candidates examined, the batch-based collision probability estimation algorithm (Contribution 2) shows one refutable candidate among 10 examined, suggesting some overlap with prior sampling techniques. The core oracle contribution (Contribution 1) examined 8 candidates with none refutable, and the lower bound result (Contribution 3) examined 6 candidates with none refutable. The limited search scope means these statistics reflect top-semantic-match coverage rather than exhaustive field analysis. The collision estimation component appears to have more substantial prior work than the memory-constrained oracle framework itself.

Given the sparse taxonomy leaf and limited refutation signals across most contributions, the work appears to occupy a relatively novel position within the constrained search scope. The explicit memory-time trade-off characterization and sub-√n memory regimes represent a clear departure from standard oracle designs. However, the analysis covers approximately 24 papers from semantic search, leaving open whether deeper literature exploration would reveal additional overlapping work in related algorithmic frameworks or theoretical computer science venues.

Taxonomy

Core-task Taxonomy Papers
15
3
Claimed Contributions
24
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: sublinear spectral clustering with memory constraints. The field addresses the challenge of partitioning large-scale graphs or datasets when both computational time and memory are severely limited. The taxonomy organizes research into four main branches. Sublinear-Time Clustering Oracles focus on query-based models that answer cluster membership questions without processing the entire input, often trading preprocessing cost against per-query efficiency. Sequential and Streaming Approaches handle data that arrives incrementally or cannot be stored in full, exemplified by works like Streaming Spectral Clustering[2] and Sequential Spectral Clustering[7]. Memory-Efficient Batch Methods develop techniques such as column sampling and locality-sensitive hashing to reduce space usage while processing the whole dataset, as seen in Column Sampling Clustering[9] and Locality Sensitive Hashing[10]. Theoretical Foundations and Cross-Domain Extensions explore privacy-preserving variants, multiscale strategies, and algorithmic guarantees that span multiple problem settings. Within the oracle-based branch, a particularly active line of work investigates memory-time trade-offs: how much preprocessing and storage one must invest to achieve fast query responses. Sublinear Spectral Oracle[0] sits squarely in this cluster, emphasizing oracles that balance preprocessing overhead with per-query complexity under strict memory budgets. It shares thematic ground with Spectral Clustering Oracles[3] and Improved Preprocessing Oracle[5], both of which also study preprocessing strategies and query efficiency. Compared to these neighbors, Sublinear Spectral Oracle[0] appears to push further on explicit memory constraints, exploring regimes where even moderate storage is unavailable. Meanwhile, works like Memory Scalability Spectral[6] and Dual Memory Clustering[14] tackle related scalability questions in batch or hybrid settings, highlighting an ongoing tension between oracle flexibility and the practicality of storing auxiliary structures.

Claimed Contributions

Sublinear spectral clustering oracle with memory-time trade-off

The authors design a spectral clustering oracle that breaks the previous Ω(√n) memory barrier by introducing a flexible trade-off between memory usage S and query time T, achieving S·T = Õ(n) for well-clusterable graphs. This allows constructing the data structure D with substantially less memory while maintaining sublinear query times.

8 retrieved papers
Batch-based collision probability estimation algorithm

The authors introduce a new batch-based estimation strategy (ESTCOLLIPROB) that partitions random walks into batches to estimate collision probabilities of random walk distributions. This technique enables the memory-efficient dot product oracle that underlies their clustering oracle, achieving the desired space-time trade-off.

10 retrieved papers
Can Refute
Nearly tight lower bound for 1-cluster vs. 2-cluster distinction

The authors establish a space-time lower bound S·T = Ω(n) for distinguishing between single-cluster expanders and two-cluster graphs using random walk queries. This lower bound demonstrates that their upper bound trade-off is nearly optimal up to polylogarithmic factors for collision-probability-based approaches.

6 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Sublinear spectral clustering oracle with memory-time trade-off

The authors design a spectral clustering oracle that breaks the previous Ω(√n) memory barrier by introducing a flexible trade-off between memory usage S and query time T, achieving S·T = Õ(n) for well-clusterable graphs. This allows constructing the data structure D with substantially less memory while maintaining sublinear query times.

Contribution

Batch-based collision probability estimation algorithm

The authors introduce a new batch-based estimation strategy (ESTCOLLIPROB) that partitions random walks into batches to estimate collision probabilities of random walk distributions. This technique enables the memory-efficient dot product oracle that underlies their clustering oracle, achieving the desired space-time trade-off.

Contribution

Nearly tight lower bound for 1-cluster vs. 2-cluster distinction

The authors establish a space-time lower bound S·T = Ω(n) for distinguishing between single-cluster expanders and two-cluster graphs using random walk queries. This lower bound demonstrates that their upper bound trade-off is nearly optimal up to polylogarithmic factors for collision-probability-based approaches.

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