N-Wise Test Data Generation

N-wise generation creates a covering set for enum columns. For a selected value of n, every value tuple across every group of n enum columns should appear at least once.

The Generate Combinations dialog only offers valid n values: from 2 up to the number of enum columns in the current schema.

Non-enum columns are still generated normally for each emitted combination row. Only enum columns participate in the finite n-wise coverage model.

When to use n-wise generation

Use n-wise generation when:

• You have two or more enum fields with finite value sets.
• You want systematic coverage of value interactions.
• Full Cartesian generation would create too many rows.
• You want to compare pairwise, 3-wise, 4-wise, or stronger coverage before choosing the right test-data volume.

For n = 2, the generator covers every pair of enum values across every pair of enum columns. For n = 3, it covers every triplet, and so on. When n equals the number of enum columns, the result is full Cartesian coverage for those enum columns.

Strategies

The dialog orders available strategies by the lowest-row evidence from the current comparison scenarios for the selected n. The best row-count choice can change by strength, so the order changes when you change n.

Strategy	Available for	When to pick it	References
Greedy	2-wise and higher	Pick as the general default for low rows with low runtime. It led the current 3-wise and 5-wise samples overall.	Greedy covering-array family
IPOG-style	2-wise and higher	Pick for predictable low runtime at higher strengths. It tracked Greedy closely and tied it on some larger samples.	NIST IPOG
AETG-style	2-wise and higher	Pick when you can spend more runtime to chase compact output. It was strongest for 4-wise row count in the samples.	AETG reference summary
PICT-inspired GCD	2-wise and higher	Pick for 2-wise when row count matters. It produced the fewest pairwise rows in the current comparison samples.	Microsoft PICT
Bach AllPairs	2-wise only	Pick for 2-wise when you want Bach Allpairs-style pair-frequency balancing. It targets lower row counts than the simple legacy pairwise algorithm while staying fast.	James Bach Satisfice AllPairs
Hypergraph vertex	2-wise and higher	Pick as the graph-informed comparator that stays closer on rows than compatibility graph, with higher runtime.	Covering arrays on hypergraphs
Compatibility graph	2-wise and higher	Pick for comparison against graph-style compatibility scoring. It was usually behind the best row-count choices.	NIST covering arrays
Pairwise (simple)	2-wise only	Pick for legacy-compatible 2-wise output. It is stable and familiar, though PICT, AETG, and Bach AllPairs used fewer rows in sample runs.	NIST covering arrays

Scenario 6x3 Data Set

For Cartesian all combinations the number of rows would be 729.

P1
enum("1.1","1.2","1.3")
P2
enum("2.1","2.2","2.3")
P3
enum("3.1","3.2","3.3")
P4
enum("4.1","4.2","4.3")
P5
enum("5.1","5.2","5.3")
P6
enum("6.1","6.2","6.3")

Scenario 6x3 - Strength 2

Algorithm	Rows	Total tuples	Covered tuples	Coverage %	Runtime ms
pict-gcd	13	135	135	100.0	2
aetg	14	135	135	100.0	10
hypergraph-vertex	14	135	135	100.0	6
compatibility-graph	16	135	135	100.0	3
bach-allpairs	16	135	135	100.0	n/a
greedy	17	135	135	100.0	2
ipog	17	135	135	100.0	1
pairwise	17	135	135	100.0	n/a

Scenario 6x3 - Strength 3

Algorithm	Rows	Total tuples	Covered tuples	Coverage %	Runtime ms
aetg	45	540	540	100.0	36
greedy	48	540	540	100.0	3
pict-gcd	48	540	540	100.0	4
hypergraph-vertex	50	540	540	100.0	21
compatibility-graph	51	540	540	100.0	21
ipog	58	540	540	100.0	2

Scenario 6x3 - Strength 4

Algorithm	Rows	Total tuples	Covered tuples	Coverage %	Runtime ms
aetg	134	1215	1215	100.0	90
greedy	137	1215	1215	100.0	10
hypergraph-vertex	141	1215	1215	100.0	145
pict-gcd	142	1215	1215	100.0	8
compatibility-graph	153	1215	1215	100.0	100
ipog	169	1215	1215	100.0	4

Scenario 6x3 - Strength 5

Algorithm	Rows	Total tuples	Covered tuples	Coverage %	Runtime ms
greedy	288	1458	1458	100.0	4
aetg	308	1458	1458	100.0	108
ipog	318	1458	1458	100.0	4
hypergraph-vertex	330	1458	1458	100.0	421
pict-gcd	331	1458	1458	100.0	6
compatibility-graph	368	1458	1458	100.0	405

Scenario 6x3 - Strength 6

Algorithm	Rows	Total tuples	Covered tuples	Coverage %	Runtime ms
aetg	729	729	729	100.0	0
compatibility-graph	729	729	729	100.0	1
greedy	729	729	729	100.0	0
hypergraph-vertex	729	729	729	100.0	1
ipog	729	729	729	100.0	0
pict-gcd	729	729	729	100.0	0

Scenario 6x4 Data Set

For Cartesian all combinations the number of rows would be 4096.

P1
enum("1.1","1.2","1.3","1.4")
P2
enum("2.1","2.2","2.3","2.4")
P3
enum("3.1","3.2","3.3","3.4")
P4
enum("4.1","4.2","4.3","4.4")
P5
enum("5.1","5.2","5.3","5.4")
P6
enum("6.1","6.2","6.3","6.4")

Scenario 6x4 - Strength 2

Algorithm	Rows	Total tuples	Covered tuples	Coverage %	Runtime ms
aetg	23	240	240	100.0	18
pict-gcd	23	240	240	100.0	3
compatibility-graph	24	240	240	100.0	4
hypergraph-vertex	26	240	240	100.0	6
bach-allpairs	28	240	240	100.0	n/a
greedy	28	240	240	100.0	1
ipog	28	240	240	100.0	1
pairwise	28	240	240	100.0	n/a

Scenario 6x4 - Strength 3

Algorithm	Rows	Total tuples	Covered tuples	Coverage %	Runtime ms
greedy	64	1280	1280	100.0	4
ipog	64	1280	1280	100.0	3
aetg	105	1280	1280	100.0	112
pict-gcd	110	1280	1280	100.0	11
hypergraph-vertex	115	1280	1280	100.0	122
compatibility-graph	120	1280	1280	100.0	60

Scenario 6x4 - Strength 4

Algorithm	Rows	Total tuples	Covered tuples	Coverage %	Runtime ms
aetg	420	3840	3840	100.0	320
pict-gcd	440	3840	3840	100.0	25
hypergraph-vertex	446	3840	3840	100.0	2184
greedy	448	3840	3840	100.0	29
ipog	448	3840	3840	100.0	14
compatibility-graph	495	3840	3840	100.0	1017

Scenario 6x4 - Strength 5

Algorithm	Rows	Total tuples	Covered tuples	Coverage %	Runtime ms
greedy	1024	6144	6144	100.0	23
ipog	1024	6144	6144	100.0	23
aetg	1335	6144	6144	100.0	1477
hypergraph-vertex	1375	6144	6144	100.0	11946
pict-gcd	1414	6144	6144	100.0	89
compatibility-graph	1534	6144	6144	100.0	9611

Scenario 6x4 - Strength 6

Algorithm	Rows	Total tuples	Covered tuples	Coverage %	Runtime ms
aetg	4096	4096	4096	100.0	2
compatibility-graph	4096	4096	4096	100.0	2
greedy	4096	4096	4096	100.0	3
hypergraph-vertex	4096	4096	4096	100.0	3
ipog	4096	4096	4096	100.0	3
pict-gcd	4096	4096	4096	100.0	3