XCSP 2.1 Benchmark Database

Instance: normalized-half-n25-d5-e56-r7-3
Number of variables: 25
Number of constraints: 56
Satisfiable: True
Timestamp: 2025-07-15 13:00:07
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 25
Number of constraints: 56

General features

Coarse blocks: 271,094
Value tables: 564

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Arity 7 7 7.00 7.00 392 MAX VALUE 108.97 0.00 0.00 0.00

Coarse blocks size 1 11,569 273.05 64.00 74,021,200 MAX VALUE 1,147,950.00 750.96 2.75 5.47

Relational linkage 0.01 0.92 0.43 0.45 54,068.40 0.00 -111,013.00 0.12 0.27 4.61

Tightness 0.42 0.60 0.49 0.49 27.35 0.00 -40.29 0.04 0.07 4.03

Tuples 31,090 45,380 39,975.20 40,177.00 2,238,610 MAX VALUE 593.23 2,822.99 0.07 4.03

Values 5 5 5.00 5.00 125 2.98e+17 40.24 0.00 0.00 0.00

Value table constraints 2 19 3.28 2.00 1,851 MAX VALUE 573.22 2.76 0.84 1.40

Value table partitions 5 3,125 222.69 125.00 125,600 MAX VALUE 2,464.05 514.10 2.31 1.22

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	7	7	7.00	7.00	392	MAX VALUE	108.97	0.00	0.00	0.00
Coarse blocks size	1	11,569	273.05	64.00	74,021,200	MAX VALUE	1,147,950.00	750.96	2.75	5.47
Relational linkage	0.01	0.92	0.43	0.45	54,068.40	0.00	-111,013.00	0.12	0.27	4.61
Tightness	0.42	0.60	0.49	0.49	27.35	0.00	-40.29	0.04	0.07	4.03
Tuples	31,090	45,380	39,975.20	40,177.00	2,238,610	MAX VALUE	593.23	2,822.99	0.07	4.03
Values	5	5	5.00	5.00	125	2.98e+17	40.24	0.00	0.00	0.00
Value table constraints	2	19	3.28	2.00	1,851	MAX VALUE	573.22	2.76	0.84	1.40
Value table partitions	5	3,125	222.69	125.00	125,600	MAX VALUE	2,464.05	514.10	2.31	1.22

Tree decomposition

Number of clusters: 2
Number of leaves: 1
Tree depth: 1
CIR: None
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/Tree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 41 43 42.00 42.00 84 1,763 7.47 1.00 0.02 0.69

Variables per cluster 24 24 24.00 24.00 48 576 6.36 0.00 0.00 0.00

Separator constraints 0 28 14.00 14.00 28 0 None 14.00 1.00 0.69

Separator variables 0 23 11.50 11.50 23 0 None 11.50 1.00 0.69

Clusters per var 1 2 1.92 2.00 48 8,388,610 15.94 0.27 0.14 0.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	41	43	42.00	42.00	84	1,763	7.47	1.00	0.02	0.69
Variables per cluster	24	24	24.00	24.00	48	576	6.36	0.00	0.00	0.00
Separator constraints	0	28	14.00	14.00	28	0	None	14.00	1.00	0.69
Separator variables	0	23	11.50	11.50	23	0	None	11.50	1.00	0.69
Clusters per var	1	2	1.92	2.00	48	8,388,610	15.94	0.27	0.14	0.28

Dual tree decomposition

Number of clusters: 4
Number of leaves: 2
Tree depth: 2
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/DualTree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 1,063 1,298 1,178.25 1,176.00 4,713 1.91e+12 28.28 84.69 0.07 1.39

Variables per cluster 48 53 50.50 50.50 202 6,487,200 15.69 1.80 0.04 1.39

Separator constraints 0 1,150 817.50 1,060.00 3,270 0 None 474.43 0.58 1.39

Separator variables 0 50 36.50 48.00 146 0 None 21.10 0.58 1.39

Clusters per variable 1 4 3.61 4.00 202 2.03e+30 69.79 0.77 0.21 0.80

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,063	1,298	1,178.25	1,176.00	4,713	1.91e+12	28.28	84.69	0.07	1.39
Variables per cluster	48	53	50.50	50.50	202	6,487,200	15.69	1.80	0.04	1.39
Separator constraints	0	1,150	817.50	1,060.00	3,270	0	None	474.43	0.58	1.39
Separator variables	0	50	36.50	48.00	146	0	None	21.10	0.58	1.39
Clusters per variable	1	4	3.61	4.00	202	2.03e+30	69.79	0.77	0.21	0.80

Primal graph

Density: 99.00%
MCB compute time (ms): 5
MCB cycles: 284
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/Primal1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.99 0.99 0.99 0.99 24.75 0.77 -0.26 0.00 0.00 0.55

Degree 23 24 23.76 24.00 594 2.48e+34 79.20 0.43 0.02 0.55

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 852 MAX VALUE 312.01 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.99	0.99	0.99	0.99	24.75	0.77	-0.26	0.00	0.00	0.55
Degree	23	24	23.76	24.00	594	2.48e+34	79.20	0.43	0.02	0.55
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	852	MAX VALUE	312.01	0.00	0.00	0.00

Triangulated primal graph

Density: 99.67%
MCB compute time (ms): 4
MCB cycles: 295
Triangles: None

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 1.00 1.00 1.00 1.00 24.92 0.92 -0.08 0.00 0.00 0.28

Degree 23 24 23.92 24.00 598 2.94e+34 79.37 0.27 0.01 0.28

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 885 MAX VALUE 324.09 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	24.92	0.92	-0.08	0.00	0.00	0.28
Degree	23	24	23.92	24.00	598	2.94e+34	79.37	0.27	0.01	0.28
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	885	MAX VALUE	324.09	0.00	0.00	0.00

Dual graph

Density: 93.70%
MCB compute time (ms): 58
MCB cycles: 1,388
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/Dual1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.93 0.94 0.94 0.94 52.44 0.03 -3.68 0.00 0.00 3.39

Degree 47 54 51.54 52.00 2,886 MAX VALUE 220.75 1.45 0.03 1.73

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 4,164 MAX VALUE 1,524.87 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.93	0.94	0.94	0.94	52.44	0.03	-3.68	0.00	0.00	3.39
Degree	47	54	51.54	52.00	2,886	MAX VALUE	220.75	1.45	0.03	1.73
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	4,164	MAX VALUE	1,524.87	0.00	0.00	0.00

Minimal dual graph

Density: 21.49%
MCB compute time (ms): 15
MCB cycles: 306

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.13 0.32 0.23 0.24 12.85 0.00 -83.38 0.04 0.18 3.30

Degree 9 17 11.82 12.00 662 MAX VALUE 137.80 1.66 0.14 1.77

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.20 3.00 979 MAX VALUE 353.72 0.40 0.12 0.50

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.13	0.32	0.23	0.24	12.85	0.00	-83.38	0.04	0.18	3.30
Degree	9	17	11.82	12.00	662	MAX VALUE	137.80	1.66	0.14	1.77
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.20	3.00	979	MAX VALUE	353.72	0.40	0.12	0.50

Triangulated dual graph

Density: 98.96%
Triangles: 26,908

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.99 1.00 0.99 0.99 55.49 0.60 -0.52 0.00 0.00 0.94

Degree 47 55 54.43 55.00 3,048 MAX VALUE 223.81 1.45 0.03 0.87

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.99	1.00	0.99	0.99	55.49	0.60	-0.52	0.00	0.00	0.94
Degree	47	55	54.43	55.00	3,048	MAX VALUE	223.81	1.45	0.03	0.87
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 60.91%

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.74 1.00 0.86 0.84 48.37 0.00 -8.45 0.08 0.10 3.55

Degree 9 47 33.50 41.00 1,876 MAX VALUE 189.57 13.46 0.40 2.90

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.74	1.00	0.86	0.84	48.37	0.00	-8.45	0.08	0.10	3.55
Degree	9	47	33.50	41.00	1,876	MAX VALUE	189.57	13.46	0.40	2.90
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 12.10%
MCB compute time (ms): 22
MCB cycles: 333
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-3/Incidence1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 7 20 9.68 7.00 784 MAX VALUE 177.43 4.25 0.44 1.26

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 1,332 MAX VALUE 461.64 0.00 0.00 0.00

XCSP 2.1 Benchmarks