BBC: Improving Large-k Approximate Nearest Neighbor Search with a Bucket-based Result Collector

Bin Cui; Gao Cong; Jinwei Zhu; Kai Zeng; Ziqi Yin

arxiv: 2604.01960 · v3 · pith:HWGQFLBNnew · submitted 2026-04-02 · 💻 cs.DB · cs.DS

BBC: Improving Large-k Approximate Nearest Neighbor Search with a Bucket-based Result Collector

Ziqi Yin , Gao Cong , Kai Zeng , Jinwei Zhu , Bin Cui This is my paper

Pith reviewed 2026-05-13 20:43 UTC · model grok-4.3

classification 💻 cs.DB cs.DS

keywords approximate nearest neighborlarge-k queriesquantization-based indexesbucket-based collectorre-ranking algorithmsANN searchdatabase indexingperformance acceleration

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The pith

A bucket-based collector organizes ANN candidates by distance to speed up large-k queries in quantization indexes by up to 3.8 times.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Quantization-based approximate nearest neighbor methods slow down for large-k queries because standard top-k collectors incur high maintenance costs and pruning becomes less effective, forcing expensive re-ranking. The paper introduces BBC with a bucket-based result buffer that groups candidates by distance to the query, allowing faster superset maintenance and a lightweight final top-k selection. It adds two re-ranking algorithms tuned to different quantization types to shrink either the number of objects checked or the number of cache misses. Experiments on real datasets confirm speedups of up to 3.8x at recall 0.95 without accuracy loss. Readers care because many applications, from recommendation to search, routinely need dozens or hundreds of neighbors at interactive speeds.

Core claim

BBC improves quantization-based ANN indexes for large-k queries by replacing conventional top-k collectors with a bucket-based result buffer that organizes candidates into distance buckets, reducing ranking costs and cache misses while enabling lightweight final selection, together with two re-ranking algorithms that cut either candidate volume or cache misses depending on the underlying quantizer.

What carries the argument

Bucket-based result buffer that organizes candidates into buckets by distance to the query for efficient superset maintenance and top-k selection.

If this is right

Existing quantization-based ANN indexes gain substantial speed for large-k queries without altering their core structure.
Re-ranking overhead drops by limiting candidates examined or by improving memory access patterns.
Cache efficiency rises during candidate ranking and selection phases.
The same collector works across multiple quantization methods while preserving recall.
Final top-k extraction becomes a lightweight step after bucket organization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same bucket organization could be tested on non-quantization ANN indexes that also produce large candidate sets.
Applications that vary k at runtime might benefit from adaptive bucket sizing tuned to expected result cardinality.
Index designers facing high-k workloads may need to treat result collection as a first-class optimization target rather than an afterthought.
Direct measurement of cache miss rates before and after BBC on new hardware would confirm the memory-efficiency mechanism.

Load-bearing premise

Grouping candidates by distance reduces ranking costs and cache misses enough to offset the overhead of maintaining the buckets.

What would settle it

Running BBC-augmented indexes against standard large-k ANN benchmarks and measuring no reduction in query time or cache misses would disprove the acceleration claim.

Figures

Figures reproduced from arXiv: 2604.01960 by Bin Cui, Gao Cong, Jinwei Zhu, Kai Zeng, Ziqi Yin.

**Figure 3.** Figure 3: Illustration of the Proposed Bucket-based Result Collector. the number of re-ranked objects increases linearly, leading to a significant increase in the re-ranking cost, as shown in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: The probability density function (PDF) of distances between the query and data vectors on the C4 dataset. report [91] and (2) experimental validation on real-world highdimensional datasets (see Exp-4). Theorem 3.1 (Expected Mean Absolute Error). Let 𝑞, 𝑜 ∈ R 𝑑 be random vectors with norms satisfying 𝛼 < ∥𝑞∥2, ∥𝑜 ∥2 < 𝛽, and let 𝑅 = ∥𝑞−𝑜 ∥2 ∈ [0, 2𝛽] denote their Euclidean distance. Assume that 𝑅 has a sub… view at source ↗

**Figure 5.** Figure 5: The accuracy-efficiency trade-off results under different 𝑘 (upper and right is better). the x86simdsort library. All experiments are run on a machine equipped with an AMD Ryzen Threadripper PRO 5965WX 7.0GHz processor (supporting AVX2) and 128 GB of RAM. 4.2 Experimental Results Exp-1: ANN Query Performance. The querying results over the four datasets are shown in [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: Relative error of large-𝑘 ANN queries on the C4 dataset (lower is better). 1 2 3 4 5 Evaluated Objects (10 6 ) 4.7 4.8 4.9 5.0 5.1 5.2 Threshold k = 5,000 1 2 3 4 5 Evaluated Objects (10 6 ) 4.8 4.9 5.0 5.1 5.2 5.3 k = 10,000 1 2 3 4 5 Evaluated Objects (10 6 ) 4.9 5.0 5.1 5.2 5.3 5.4 k = 20,000 1 2 3 4 5 Evaluated Objects (10 6 ) 5.1 5.2 5.3 5.4 5.5 5.6 k = 40,000 1 2 3 4 5 Evaluated Objects (10 6 ) 5.3 5… view at source ↗

**Figure 7.** Figure 7: Comparison of threshold values generated by the result buffer and binary heap on the C4 Dataset. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗

**Figure 8.** Figure 8: Overhead of top-𝑘 collectors under varying numbers of evaluated objects on the Deep100M dataset. achieving up to an order of magnitude improvement. For example, on the Deep100M dataset, when 𝑘 = 100,000 and 𝑛𝑝𝑟𝑜𝑏𝑒 = 210, for IVF+RaBitQ, RB takes only 2.0 ms, compared to 30.6 ms for Heap and 12.3 ms for Lazy, achieving an order-of-magnitude speedup. (2) RB remains efficient at higher values of 𝑘, while Lazy… view at source ↗

**Figure 9.** Figure 9: Re-ranking Time and Number of Re-ranked Objects on the C4 Dataset [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗

**Figure 10.** Figure 10: Top-𝑘 collection time under different numbers of evaluated objects on the Deep100M dataset [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗

read the original abstract

Although Approximate Nearest Neighbor (ANN) search has been extensively studied, large-k ANN queries that aim to retrieve a large number of nearest neighbors remain underexplored, despite their numerous real-world applications. Existing ANN methods face significant performance degradation for such queries. In this work, we first investigate the reasons for the performance degradation of quantization-based ANN indexes: (1) the inefficiency of existing top-k collectors, which incurs significant overhead in candidate maintenance, and (2) the reduced pruning effectiveness of quantization methods, which leads to a costly re-ranking process. To address this, we propose a novel bucket-based result collector (BBC) to enhance the efficiency of existing quantization-based ANN indexes for large-k ANN queries. BBC introduces two key components: (1) a bucket-based result buffer that organizes candidates into buckets by their distances to the query. This design reduces ranking costs and improves cache efficiency, enabling high performance maintenance of a candidate superset and a lightweight final selection of top-k results. (2) two re-ranking algorithms tailored for different types of quantization methods, which accelerate their re-ranking process by reducing either the number of candidate objects to be re-ranked or cache misses. Extensive experiments on real-world datasets demonstrate that BBC accelerates existing quantization-based ANN methods by up to 3.8x at recall@k = 0.95 for large-k ANN queries.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

BBC swaps top-k heaps for distance buckets plus two custom re-rankers and reports up to 3.8x speedup on large-k ANN over existing quantization indexes.

read the letter

BBC replaces the standard top-k collector with a distance-bucketed buffer and adds two quantization-specific re-rankers. That change is what lets it claim up to 3.8x faster large-k ANN at 0.95 recall on top of existing indexes. The paper does a good job laying out why current top-k maintenance and re-ranking hurt when k gets large: heaps get expensive and quantization pruning weakens. The bucket idea groups candidates so you can do lighter final selection and better cache behavior. The tailored re-rankers cut the number of full distance computations or misses for different quantizers. Experiments on real datasets back the speedups, and the design avoids new hyperparameters. The soft spot is whether the bucket insertion and maintenance cost stays low enough when the candidate superset is big. The stress-test note points out that if pruning is already weak, the linear work on buckets might eat the gains, and there's no analytic bound shown. I'd want to see per-component timings and results across a wider range of k and recall targets to be sure the improvement holds generally. This is useful for anyone running large-k ANN in production databases or analytics systems. A reader who maintains or extends quantization indexes will get concrete ideas to try. It deserves a serious referee because the core technique is new, the problem is real, and the reported gains are substantial even if the evaluation could be tighter on overheads.

Referee Report

2 major / 1 minor

Summary. The paper proposes BBC, a bucket-based result collector, to address performance degradation in quantization-based ANN indexes for large-k queries. It identifies two issues—inefficient top-k candidate maintenance and reduced pruning effectiveness leading to costly re-ranking—and introduces a distance-bucketed buffer for candidate organization plus two tailored re-ranking algorithms. Experiments on real-world datasets are reported to yield speedups of up to 3.8× at recall@k = 0.95.

Significance. If the claimed speedups are robustly verified with full experimental controls, the work would offer a practical, low-overhead enhancement to existing quantization indexes without altering their core structure. This could benefit database applications involving large-k retrieval (e.g., recommendation or analytics workloads) by improving cache behavior and reducing ranking costs in the high-candidate regime.

major comments (2)

[Abstract] Abstract: the central performance claim of up to 3.8× speedup at recall@k=0.95 is presented without any description of datasets, quantization methods, baselines, number of trials, or variance; this leaves the offset between bucket-maintenance overhead and saved ranking/cache work unverifiable, especially for the large-superset regime the method targets.
[Abstract] The design rationale (bucket insertion and re-ranking) assumes that organizing candidates by distance reduces ranking costs enough to offset linear bucket-maintenance overhead; no analytic bound or worst-case analysis is supplied for the case when quantization pruning returns a very large candidate superset, which is precisely the operating point emphasized in the paper.

minor comments (1)

[Abstract] The abstract would benefit from a brief statement of the range of k values tested and the specific recall@k target used for the 3.8× figure.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on the abstract and the request for stronger analytical support. We address each major comment below and will revise the manuscript to improve clarity and verifiability of the claims.

read point-by-point responses

Referee: [Abstract] Abstract: the central performance claim of up to 3.8× speedup at recall@k=0.95 is presented without any description of datasets, quantization methods, baselines, number of trials, or variance; this leaves the offset between bucket-maintenance overhead and saved ranking/cache work unverifiable, especially for the large-superset regime the method targets.

Authors: We agree that the abstract would benefit from additional context to make the speedup claim more self-contained. In the revision we will expand the abstract with a brief clause noting that the results are obtained on standard real-world datasets using common quantization-based indexes (with full details on baselines, number of trials, and variance reported in the experimental section). Due to strict length limits we cannot embed every experimental parameter in the abstract itself, but the added sentence will allow readers to immediately locate the supporting evidence and verify the net benefit of bucket maintenance versus ranking savings. revision: partial
Referee: [Abstract] The design rationale (bucket insertion and re-ranking) assumes that organizing candidates by distance reduces ranking costs enough to offset linear bucket-maintenance overhead; no analytic bound or worst-case analysis is supplied for the case when quantization pruning returns a very large candidate superset, which is precisely the operating point emphasized in the paper.

Authors: We acknowledge that a formal analytic bound would strengthen the design rationale. The current manuscript supplies extensive empirical measurements (Section 5) across increasing candidate-superset sizes that demonstrate the bucket-maintenance cost is more than offset by reduced ranking and cache-miss overhead. In the revision we will add a short cost-model paragraph in the design section that contrasts the amortized O(1) bucket insertion with the O(n log n) cost of full sorting or the full re-ranking scan, and we will explicitly discuss the regime where the superset size greatly exceeds k. While a complete worst-case proof is not provided, the added model together with the existing empirical data will address the concern for the targeted operating point. revision: yes

Circularity Check

0 steps flagged

No circularity: structural proposal with empirical validation

full rationale

The paper identifies performance bottlenecks in quantization-based ANN for large-k queries via investigation, then introduces BBC as a bucket-organized buffer plus two re-ranking algorithms. No equations, parameter fits, or derivations are present that reduce to inputs by construction. No self-citations serve as load-bearing uniqueness theorems or ansatzes. The speedup claims rest on experimental measurements rather than self-referential logic, satisfying the self-contained criterion.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are stated in the abstract; the approach builds on standard quantization-based ANN indexes and common cache/ranking assumptions.

pith-pipeline@v0.9.0 · 5550 in / 986 out tokens · 51648 ms · 2026-05-13T20:43:39.806837+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

BBC introduces a bucket-based result buffer that organizes candidates into buckets by their distances to the query... reduces ranking costs and improves cache efficiency
IndisputableMonolith/Foundation/DimensionForcing.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

two re-ranking algorithms tailored for different types of quantization methods

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Forward citations

Cited by 1 Pith paper

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