SQL-FRONTIER Benchmark Deep-Dive / Vector & Embeddings / task_035_Q35_kmeans_cluster_assignment_step
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✔ PASS Vector & Embeddings task_035_Q35_kmeans_cluster_assignment_step Scaled: 1M+ Records Ordered: Yes

K-Means Clustering Assignment and Centroid Update in Pure SQL

Candidate Latency (1M Rows)
299.07 ms
(1.2x slower than golden)
Golden Latency (1M Rows)
247.68 ms
DuckDB in-memory engine
Underlying Data Volume
1,000,002 rows
11.4 MiB across 2 tables
Evaluated Model
gemini-3.8-flash-low
Gen Latency: 8.5s
✔ Correctness Verified on 1M+ Records
Candidate SQL output matches ground truth golden query across all multiset rows and numeric tolerances (tol=1e-3). Zero data skew or anti-patterns detected on full dataset scale.

1. Analytical Significance & What It Means

Scenario & Frontier Trap
Business Scenario & Problem

Unsupervised customer segmentation can be run directly inside DuckDB by assigning customer vectors to the nearest centroid and recomputing cluster means in a single query.

⚡ The Frontier Trap (Why LLMs Fail)

Running ML clustering outside the warehouse requires exporting millions of vectors over the network.

Prompt / User Request Given to Model
Unsupervised customer segmentation can be run directly inside DuckDB by assigning customer vectors to the nearest centroid and recomputing cluster means in a single query.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: point_id, assigned_cluster, distance_to_center.
Results should be ordered as specified.

2. Underlying Tables, Row Counts & Data Volume

2 Tables (1,000,002 rows • 11.4 MiB)

Production-scale fixtures loaded into the isolated DuckDB sandbox with at least 1,000,000 records per table:

📊 cluster_centroids 2 rows 24 B Data Volume
cluster_id (INTEGER) center (FLOAT[2])
Data Preview (showing sample rows from 2 total rows):
# cluster_id center
1 1 [1. 1.]
2 2 [8. 8.]
📊 data_points 1,000,000 rows 11.4 MiB Data Volume
point_id (INTEGER) coord (FLOAT[2])
Data Preview (showing sample rows from 1,000,000 total rows):
# point_id coord
1 101 [1.2 0.9]
2 102 [1.5 1.1]
3 103 [7.8 8.2]
4 103 [0.8574 0.1446]
5 104 [0.8993 0.0794]
6 105 [0.8334 0.1199]
7 106 [0.8301 0.0396]
8 107 [0.8783 0.0938]
9 108 [0.8903 0.0906]
10 109 [0.8561 0.0733]
11 110 [0.8377 0.1094]
12 111 [0.8605 0.1795]
13 112 [0.8533 0.1679]
14 113 [0.9249 0.1086]
15 114 [0.8603 0.1379]

3. Graphical Query Execution Plan & Cost Bottlenecks

Physical Operator Tree (DuckDB 2.0 Profiler)

Visual flowchart of the physical execution pipeline. Operators with high relative costs (≥ 20% of query runtime or heavy latency) are visually highlighted:

Pipeline Latency Distribution (Total Plan Time: 1115.24 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders
📐 PROJECTION 0.0%
Latency: 0.29 ms
Rows In/Out: 999,999
Data Vol: 11.44 MB
📁 Projections: ['#0', 'CAST(#1 AS ...
⏳ ORDER_BY 🔥 6.8% Cost
Latency: 75.30 ms
Rows In/Out: 999,999
Data Vol: 8.58 MB
⚠️ Heavy Execution Bottleneck (6.8% of query runtime)
📐 PROJECTION 0.1%
Latency: 0.66 ms
Rows In/Out: 999,999
Data Vol: 8.58 MB
📁 Projections: ['#0', 'CAST(#1 AS ...
📐 PROJECTION 3.3%
Latency: 36.97 ms
Rows In/Out: 999,999
Data Vol: 11.44 MB
📁 Projections: ['point_id', 'assig...
📐 PROJECTION 2.0%
Latency: 21.80 ms
Rows In/Out: 999,999
Data Vol: 11.44 MB
📁 Projections: ['point_id', 'clust...
📐 PROJECTION 0.2%
Latency: 1.82 ms
Rows In/Out: 999,999
Data Vol: 22.89 MB
📁 Projections: ['#0', '#[1.1]', '#...
📊 HASH_GROUP_BY 🔥 84.0% Cost
Latency: 937.21 ms
Rows In/Out: 999,999
Data Vol: 22.89 MB
⚠️ Heavy Execution Bottleneck (84.0% of query runtime)
📐 PROJECTION 3.0%
Latency: 33.03 ms
Rows In/Out: 2,000,000
Data Vol: 53.41 MB
📁 Projections: ['point_id', 'struc...
⚙️ CROSS_PRODUCT 0.3%
Latency: 3.04 ms
Rows In/Out: 2,000,000
Data Vol: 45.78 MB
🔍 TABLE_SCAN 0.5%
Latency: 5.12 ms
Rows In/Out: 1,000,000
Data Vol: 11.44 MB
📁 memory.main.data_points
🔍 TABLE_SCAN 0.0%
Latency: 0.01 ms
Rows In/Out: 2
Data Vol: 24 B
📁 memory.main.cluster_centroids
Operator Cost % Latency Processed Rows Data Volume Details / Table Status
HASH_GROUP_BY 84.0% 937.21 ms 999,999 22.89 MB - 🔥 BOTTLENECK
ORDER_BY 6.8% 75.30 ms 999,999 8.58 MB - 🔥 BOTTLENECK
PROJECTION 3.3% 36.97 ms 999,999 11.44 MB Projections: ['point_id', 'assigned_cluster', 'd Normal
PROJECTION 3.0% 33.03 ms 2,000,000 53.41 MB Projections: ['point_id', 'struct_pack(#[1.1], # Normal
PROJECTION 2.0% 21.80 ms 999,999 11.44 MB Projections: ['point_id', 'cluster_id', 'dist'] Normal
TABLE_SCAN 0.5% 5.12 ms 1,000,000 11.44 MB memory.main.data_points Normal
CROSS_PRODUCT 0.3% 3.04 ms 2,000,000 45.78 MB - Normal
PROJECTION 0.2% 1.82 ms 999,999 22.89 MB Projections: ['#0', '#[1.1]', '#[2.0]', '#[2.1]' Normal
PROJECTION 0.1% 0.66 ms 999,999 8.58 MB Projections: ['#0', 'CAST(#1 AS TINYINT)', '#2'] Normal
PROJECTION 0.0% 0.29 ms 999,999 11.44 MB Projections: ['#0', 'CAST(#1 AS INTEGER)', '#2'] Normal
TABLE_SCAN 0.0% 0.01 ms 2 0.00 MB memory.main.cluster_centroids Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted
Candidate SQL Executed by gemini-3.8-flash-low (Runtime on 1M Rows: 299.07 ms) 
WITH point_distances AS
  (SELECT p.point_id,
          p.coord,
          c.cluster_id,
          array_distance(p.coord, c.center) AS dist,
          row_number() OVER (PARTITION BY p.point_id
                             ORDER BY array_distance(p.coord, c.center) ASC) AS rank_closest
   FROM data_points p
   CROSS JOIN cluster_centroids c)
SELECT point_id,
       cluster_id AS assigned_cluster,
       round(dist, 4) AS distance_to_center
FROM point_distances
WHERE rank_closest = 1
ORDER BY point_id;
Golden Reference Ground Truth SQL (Runtime on 1M Rows: 247.68 ms) 
-- Step 1: Assign each point to the closest cluster centroid via array_distance
 WITH point_distances AS
  (SELECT p.point_id,
          p.coord,
          c.cluster_id,
          array_distance(p.coord, c.center) AS dist,
          row_number() OVER (PARTITION BY p.point_id
                             ORDER BY array_distance(p.coord, c.center) ASC) AS rank_closest
   FROM data_points p
   CROSS JOIN cluster_centroids c)
SELECT point_id,
       cluster_id AS assigned_cluster,
       round(dist, 4) AS distance_to_center
FROM point_distances
WHERE rank_closest = 1
ORDER BY point_id;
DuckDB Fixture Setup DDL & Data Population 
CREATE TABLE cluster_centroids (cluster_id INT, center FLOAT[2]);


CREATE TABLE data_points (point_id INT, coord FLOAT[2]);


INSERT INTO cluster_centroids
VALUES (1, [1.0, 1.0]::FLOAT[2]),
       (2, [8.0, 8.0]::FLOAT[2]);


INSERT INTO data_points
VALUES (101, [1.2, 0.9]::FLOAT[2]),
       (102, [1.5, 1.1]::FLOAT[2]),
       (103, [7.8, 8.2]::FLOAT[2]);

5. Query Results & Expected Ground Truth

Tabular Comparison
Actual Candidate Output (999,999 rows × 3 cols)
# point_id assigned_cluster distance_to_center
1 101 1 0.2236
2 102 1 0.5099
3 103 2 0.2828
4 104 1 0.9261
5 105 1 0.8957
6 106 1 0.9753
7 107 1 0.9143
8 108 1 0.916
9 109 1 0.9378
10 110 1 0.9053
11 111 1 0.8323
12 112 1 0.8449
13 113 1 0.8946
14 114 1 0.8733
15 115 1 0.8929
16 116 1 0.9036
17 117 1 0.8931
18 118 1 0.9855
19 119 1 0.8941
20 120 1 0.9181
21 121 1 0.9524
22 122 1 0.8884
23 123 1 0.9468
24 124 1 0.8639
25 125 1 0.8921
Showing first 25 of 999,999 total rows.
Expected Golden Output (999,999 rows × 3 cols)
# point_id assigned_cluster distance_to_center
1 101 1 0.2236
2 102 1 0.5099
3 103 2 0.2828
4 104 1 0.9261
5 105 1 0.8957
6 106 1 0.9753
7 107 1 0.9143
8 108 1 0.916
9 109 1 0.9378
10 110 1 0.9053
11 111 1 0.8323
12 112 1 0.8449
13 113 1 0.8946
14 114 1 0.8733
15 115 1 0.8929
16 116 1 0.9036
17 117 1 0.8931
18 118 1 0.9855
19 119 1 0.8941
20 120 1 0.9181
21 121 1 0.9524
22 122 1 0.8884
23 123 1 0.9468
24 124 1 0.8639
25 125 1 0.8921
Showing first 25 of 999,999 total rows.
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