✔ PASS Search & Retrieval task_073_Q73_search_term_cooccurrence_matrix Scaled: 1M+ Records Ordered: Yes

Search Term Co-Occurrence Matrix (Market Basket of Search Queries)

Candidate Latency (1M Rows)

0.87 ms

(1.1x faster than golden)

Golden Latency (1M Rows)

0.92 ms

DuckDB in-memory engine

Underlying Data Volume

2,500 rows

58.6 KiB across 1 table

Evaluated Model

gemini-3.8-flash-low

Gen Latency: 12.8s

✔ 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

To suggest related searches, engines analyze queries searched together in the same session (e.g. users searching 'monitor' also search 'hdmi cable' 42% of the time).

⚡ The Frontier Trap (Why LLMs Fail)

Self-joining search sessions without ordering (`a.term < b.term`) doubles matrix size with duplicate reversed pairs.

Prompt / User Request Given to Model

To suggest related searches, engines analyze queries searched together in the same session (e.g. users searching 'monitor' also search 'hdmi cable' 42% of the time).

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: term_a, term_b, cooccurrence_count.
Results should be ordered as specified.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (2,500 rows • 58.6 KiB)

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

📊 session_searches 2,500 rows 58.6 KiB Data Volume

session_id (INTEGER) term (VARCHAR)

Data Preview (showing sample rows from 2,500 total rows):

#	session_id	term
1	1	laptop
2	1	mouse
3	1	backpack
4	2	laptop
5	2	mouse
6	3	laptop
7	3	keyboard
8	3	laptop
9	4	mouse
10	5	backpack
11	6	keyboard
12	7	laptop
13	8	mouse
14	9	backpack
15	10	keyboard

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: 0.87 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders

📐 PROJECTION 0.3%

Latency: 0.00 ms

Rows In/Out: 4

Data Vol: 160 B

📁 Projections: ['__internal_decomp...

⏳ ORDER_BY 20.2%

Latency: 0.18 ms

Rows In/Out: 4

Data Vol: 160 B

📐 PROJECTION 0.5%

Latency: 0.00 ms

Rows In/Out: 4

Data Vol: 160 B

📁 Projections: ['__internal_compre...

📐 PROJECTION 1.0%

Latency: 0.01 ms

Rows In/Out: 4

Data Vol: 160 B

📁 Projections: ['__internal_decomp...

📊 HASH_GROUP_BY 20.7%

Latency: 0.18 ms

Rows In/Out: 4

Data Vol: 160 B

📐 PROJECTION 0.0%

Latency: 0.00 ms

Rows In/Out: 6

Data Vol: 192 B

📁 Projections: ['term', 'term']

📐 PROJECTION 0.3%

Latency: 0.00 ms

Rows In/Out: 6

Data Vol: 192 B

📁 Projections: ['__internal_compre...

⚡ HASH_JOIN 40.6%

Latency: 0.35 ms

Rows In/Out: 6

Data Vol: 192 B

🔍 TABLE_SCAN 8.1%

Latency: 0.07 ms

Rows In/Out: 2,500

Data Vol: 0.05 MB

📁 memory.main.session_searches

🔍 TABLE_SCAN 8.4%

Latency: 0.07 ms

Rows In/Out: 2,500

Data Vol: 0.05 MB

📁 memory.main.session_searches

Operator	Cost %	Latency	Processed Rows	Data Volume	Details / Table	Status
HASH_JOIN	40.6%	0.35 ms	6	0.00 MB	-	Normal
HASH_GROUP_BY	20.7%	0.18 ms	4	0.00 MB	-	Normal
ORDER_BY	20.2%	0.18 ms	4	0.00 MB	-	Normal
TABLE_SCAN	8.4%	0.07 ms	2,500	0.05 MB	memory.main.session_searches	Normal
TABLE_SCAN	8.1%	0.07 ms	2,500	0.05 MB	memory.main.session_searches	Normal
PROJECTION	1.0%	0.01 ms	4	0.00 MB	Projections: ['__internal_decompress_string(#0)'	Normal
PROJECTION	0.5%	0.00 ms	4	0.00 MB	Projections: ['__internal_compress_string_uhugei	Normal
PROJECTION	0.3%	0.00 ms	4	0.00 MB	Projections: ['__internal_decompress_string(#0)'	Normal
PROJECTION	0.3%	0.00 ms	6	0.00 MB	Projections: ['__internal_compress_string_uhugei	Normal
PROJECTION	0.0%	0.00 ms	6	0.00 MB	Projections: ['term', 'term']	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

SELECT a.term AS term_a,
       b.term AS term_b,
       count(*) AS cooccurrence_count
FROM session_searches a
JOIN session_searches b ON a.session_id = b.session_id
AND a.term < b.term
GROUP BY a.term,
         b.term
ORDER BY cooccurrence_count DESC,
         term_a,
         term_b;

-- Find pairs of terms most frequently searched in the same user session

SELECT a.term AS term_a,
       b.term AS term_b,
       count(*) AS cooccurrence_count
FROM session_searches a
JOIN session_searches b ON a.session_id = b.session_id
AND a.term < b.term
GROUP BY a.term,
         b.term
ORDER BY cooccurrence_count DESC,
         term_a,
         term_b;

CREATE TABLE session_searches (session_id INT, term VARCHAR);


INSERT INTO session_searches
VALUES (1, 'laptop'),
       (1, 'mouse'),
       (1, 'backpack'),
       (2, 'laptop'),
       (2, 'mouse'),
       (3, 'laptop'),
       (3, 'keyboard');

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (4 rows × 3 cols)

#	term_a	term_b	cooccurrence_count
1	keyboard	laptop	2
2	laptop	mouse	2
3	backpack	laptop	1
4	backpack	mouse	1

Expected Golden Output (4 rows × 3 cols)

#	term_a	term_b	cooccurrence_count
1	keyboard	laptop	2
2	laptop	mouse	2
3	backpack	laptop	1
4	backpack	mouse	1

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