✔ PASS Graph & Hierarchy task_078_Q78_transitive_fraud_sybil_ring Scaled: 1M+ Records Ordered: Yes

Transitive Fraud Ring & Sybil Account Detection via Device Links

Candidate Latency (1M Rows)

1.79 ms

(1.2x slower than golden)

Golden Latency (1M Rows)

1.50 ms

DuckDB in-memory engine

Underlying Data Volume

4 rows

32 B across 1 table

Evaluated Model

gemini-3.8-flash-low

Gen Latency: 12.2s

✔ 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

Financial fraudsters create hundreds of fake accounts linked by shared credit cards, device fingerprints, or IP addresses. Finding all accounts transitively connected to a confirmed fraudster exposes the syndicate.

⚡ The Frontier Trap (Why LLMs Fail)

Looking only 1 hop away misses fraudsters who funnel funds through mule intermediary accounts.

Prompt / User Request Given to Model

Financial fraudsters create hundreds of fake accounts linked by shared credit cards, device fingerprints, or IP addresses. Finding all accounts transitively connected to a confirmed fraudster exposes the syndicate.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: seed_account, connected_account, shortest_hop_distance.
Results should be ordered as specified.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (4 rows • 32 B)

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

📊 shared_identifiers 4 rows 32 B Data Volume

account_id (INTEGER) linked_account_id (INTEGER)

Data Preview (showing sample rows from 4 total rows):

#	account_id	linked_account_id
1	101	102
2	102	103
3	103	104
4	201	202

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

⏳ ORDER_BY 9.9%

Latency: 0.18 ms

Rows In/Out: 3

Data Vol: 36 B

📊 HASH_GROUP_BY 🔥 41.9% Cost

Latency: 0.75 ms

Rows In/Out: 3

Data Vol: 36 B

📐 PROJECTION 0.1%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 36 B

📁 Projections: ['seed_account', 'c...

📊 HASH_GROUP_BY 13.7%

Latency: 0.24 ms

Rows In/Out: 3

Data Vol: 36 B

📐 PROJECTION 0.1%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 36 B

📁 Projections: ['seed_account', 'c...

🔄 RECURSIVE_CTE 25.0%

Latency: 0.45 ms

Rows In/Out: 3

Data Vol: 36 B

📐 PROJECTION 0.1%

Latency: 0.00 ms

Rows In/Out: 1

Data Vol: 12 B

📁 Projections: ['seed_account', 'c...

🔍 TABLE_SCAN 1.1%

Latency: 0.02 ms

Rows In/Out: 1

Data Vol: 4 B

📁 memory.main.shared_identifiers

📐 PROJECTION 0.3%

Latency: 0.00 ms

Rows In/Out: 2

Data Vol: 56 B

📁 Projections: ['seed_account', 'l...

⚡ HASH_JOIN 5.1%

Latency: 0.09 ms

Rows In/Out: 2

Data Vol: 56 B

🎯 FILTER 1.8%

Latency: 0.03 ms

Rows In/Out: 3

Data Vol: 36 B

🔍 RECURSIVE_CTE_SCAN 0.2%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 36 B

🔍 TABLE_SCAN 1.0%

Latency: 0.02 ms

Rows In/Out: 4

Data Vol: 32 B

📁 memory.main.shared_identifiers

Operator	Cost %	Latency	Processed Rows	Details / Table	Status
HASH_GROUP_BY	41.9%	0.75 ms	3	-	🔥 BOTTLENECK
RECURSIVE_CTE	25.0%	0.45 ms	3	-	Normal
HASH_GROUP_BY	13.7%	0.24 ms	3	-	Normal
ORDER_BY	9.9%	0.18 ms	3	-	Normal
HASH_JOIN	5.1%	0.09 ms	2	-	Normal
FILTER	1.8%	0.03 ms	3	-	Normal
TABLE_SCAN	1.1%	0.02 ms	1	memory.main.shared_identifiers	Normal
TABLE_SCAN	1.0%	0.02 ms	4	memory.main.shared_identifiers	Normal
PROJECTION	0.3%	0.00 ms	2	Projections: ['seed_account', 'linked_account_id	Normal
RECURSIVE_CTE_SCAN	0.2%	0.00 ms	3	-	Normal
PROJECTION	0.1%	0.00 ms	3	Projections: ['seed_account', 'connected_account	Normal
PROJECTION	0.1%	0.00 ms	3	Projections: ['seed_account', 'connected_account	Normal
PROJECTION	0.1%	0.00 ms	1	Projections: ['seed_account', 'connected_account	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

WITH RECURSIVE fraud_cluster AS
  (SELECT 101 AS seed_account,
          linked_account_id AS connected_account,
          1 AS hop_distance
   FROM shared_identifiers
   WHERE account_id = 101
   UNION ALL SELECT c.seed_account,
                    s.linked_account_id,
                    c.hop_distance + 1
   FROM fraud_cluster c
   JOIN shared_identifiers s ON c.connected_account = s.account_id
   WHERE c.hop_distance < 5)
SELECT DISTINCT seed_account,
                connected_account,
                min(hop_distance) AS shortest_hop_distance
FROM fraud_cluster
GROUP BY seed_account,
         connected_account
ORDER BY shortest_hop_distance;

-- Find all accounts transitively linked to known bad actor 101
 WITH RECURSIVE fraud_cluster AS
  (SELECT 101 AS seed_account,
          linked_account_id AS connected_account,
          1 AS hop_distance
   FROM shared_identifiers
   WHERE account_id = 101
   UNION ALL SELECT c.seed_account,
                    s.linked_account_id,
                    c.hop_distance + 1
   FROM fraud_cluster c
   JOIN shared_identifiers s ON c.connected_account = s.account_id
   WHERE c.hop_distance < 5)
SELECT DISTINCT seed_account,
                connected_account,
                min(hop_distance) AS shortest_hop_distance
FROM fraud_cluster
GROUP BY seed_account,
         connected_account
ORDER BY shortest_hop_distance;

CREATE TABLE shared_identifiers (account_id INT, linked_account_id INT);


INSERT INTO shared_identifiers
VALUES (101, 102),
       -- 101 shares credit card with 102
 (102, 103),
 -- 102 shares device with 103
 (103, 104),
 -- 103 shares bank account with 104
 (201, 202); -- Separate cluster

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (3 rows × 3 cols)

#	seed_account	connected_account	shortest_hop_distance
1	101	102	1
2	101	103	2
3	101	104	3

Expected Golden Output (3 rows × 3 cols)

#	seed_account	connected_account	shortest_hop_distance
1	101	102	1
2	101	103	2
3	101	104	3

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