XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-11-414-200-42-ext
Number of variables: 40
Number of constraints: 414
Satisfiable: True
Timestamp: 2025-07-27 21:30:00
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 40
Number of constraints: 414

General features

Coarse blocks: 9,108
Value tables: 40

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

Arity 2 2 2.00 2.00 828 MAX VALUE 286.96 0.00 0.00 0.00

Coarse blocks size 3 11 8.76 9.00 79,824 MAX VALUE 19,656.20 1.33 0.15 1.68

Relational linkage 0.27 0.73 0.56 0.55 244.54 0.00 -263.47 0.08 0.14 1.27

Tightness 0.12 0.31 0.20 0.21 84.15 0.00 -666.58 0.04 0.18 2.87

Tuples 83 107 96.41 96.00 39,912 MAX VALUE 1,890.95 4.42 0.05 2.87

Values 11 11 11.00 11.00 440 MAX VALUE 95.92 0.00 0.00 0.00

Value table constraints 14 25 20.70 20.50 828 MAX VALUE 120.75 3.01 0.15 2.24

Value table partitions 11 11 11.00 11.00 440 MAX VALUE 95.92 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	828	MAX VALUE	286.96	0.00	0.00	0.00
Coarse blocks size	3	11	8.76	9.00	79,824	MAX VALUE	19,656.20	1.33	0.15	1.68
Relational linkage	0.27	0.73	0.56	0.55	244.54	0.00	-263.47	0.08	0.14	1.27
Tightness	0.12	0.31	0.20	0.21	84.15	0.00	-666.58	0.04	0.18	2.87
Tuples	83	107	96.41	96.00	39,912	MAX VALUE	1,890.95	4.42	0.05	2.87
Values	11	11	11.00	11.00	440	MAX VALUE	95.92	0.00	0.00	0.00
Value table constraints	14	25	20.70	20.50	828	MAX VALUE	120.75	3.01	0.15	2.24
Value table partitions	11	11	11.00	11.00	440	MAX VALUE	95.92	0.00	0.00	0.00

Tree decomposition

Number of clusters: 11
Number of leaves: 5
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/Tree1.json

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

Cluster constraints 60 241 153.36 178.00 1,687 3.37e+23 54.17 63.44 0.41 2.40

Variables per cluster 15 30 23.18 25.00 255 7.43e+14 34.24 5.44 0.23 2.02

Separator constraints 0 220 115.73 138.00 1,273 0 None 66.72 0.58 2.40

Separator variables 0 29 19.55 23.00 215 0 None 7.95 0.41 2.15

Clusters per var 1 11 6.38 8.00 255 4.66e+28 66.01 2.99 0.47 1.99

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	60	241	153.36	178.00	1,687	3.37e+23	54.17	63.44	0.41	2.40
Variables per cluster	15	30	23.18	25.00	255	7.43e+14	34.24	5.44	0.23	2.02
Separator constraints	0	220	115.73	138.00	1,273	0	None	66.72	0.58	2.40
Separator variables	0	29	19.55	23.00	215	0	None	7.95	0.41	2.15
Clusters per var	1	11	6.38	8.00	255	4.66e+28	66.01	2.99	0.47	1.99

Dual tree decomposition

Number of clusters: 38
Number of leaves: 20
Tree depth: 5
CIR: 0.03
Independent Cluster Pairs: 17
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/DualTree1.json

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

Cluster constraints 216 3,100 850.11 568.50 32,304 MAX VALUE 247.01 683.71 0.80 3.51

Variables per cluster 29 246 77.16 48.50 2,932 MAX VALUE 157.78 55.17 0.72 3.30

Separator constraints 0 1,778 630.71 488.00 23,967 0 None 398.97 0.63 3.51

Separator variables 0 191 66.26 47.00 2,518 0 None 41.97 0.63 3.33

Clusters per variable 1 10 7.08 8.00 2,932 MAX VALUE 773.11 2.20 0.31 1.80

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	216	3,100	850.11	568.50	32,304	MAX VALUE	247.01	683.71	0.80	3.51
Variables per cluster	29	246	77.16	48.50	2,932	MAX VALUE	157.78	55.17	0.72	3.30
Separator constraints	0	1,778	630.71	488.00	23,967	0	None	398.97	0.63	3.51
Separator variables	0	191	66.26	47.00	2,518	0	None	41.97	0.63	3.33
Clusters per variable	1	10	7.08	8.00	2,932	MAX VALUE	773.11	2.20	0.31	1.80

Primal graph

Density: 53.08%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,471
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/Primal1.json

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

Clustering coefficient 0.49 0.59 0.53 0.53 21.20 0.00 -25.45 0.03 0.05 3.52

Degree 14 25 20.70 20.50 828 MAX VALUE 120.75 3.01 0.15 2.24

Eccentricity 2 2 2.00 2.00 80 1.10e+12 27.73 0.00 0.00 0.00

MCB cycle size 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	0.49	0.59	0.53	0.53	21.20	0.00	-25.45	0.03	0.05	3.52
Degree	14	25	20.70	20.50	828	MAX VALUE	120.75	3.01	0.15	2.24
Eccentricity	2	2	2.00	2.00	80	1.10e+12	27.73	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 83.33%
MCB compute time (ms): None
MCB cycles: None
Triangles: 6,401

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

Clustering coefficient 0.82 1.00 0.91 0.90 36.52 0.02 -3.69 0.05 0.05 3.11

Degree 14 39 32.50 36.00 1,300 MAX VALUE 138.04 6.75 0.21 2.17

Eccentricity 1 2 1.95 2.00 78 2.75e+11 26.34 0.22 0.11 0.20

MCB cycle size 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	0.82	1.00	0.91	0.90	36.52	0.02	-3.69	0.05	0.05	3.11
Degree	14	39	32.50	36.00	1,300	MAX VALUE	138.04	6.75	0.21	2.17
Eccentricity	1	2	1.95	2.00	78	2.75e+11	26.34	0.22	0.11	0.20
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 9.75%
MCB compute time (ms): 28,170
MCB cycles: 8,527
Triangles: 55,798
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/Dual1.json

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

Clustering coefficient 0.49 0.54 0.51 0.50 209.69 0.00 -281.68 0.01 0.02 4.84

Degree 28 48 40.28 41.00 16,674 MAX VALUE 1,527.92 4.00 0.10 2.74

Eccentricity 2 3 3.00 3.00 1,241 MAX VALUE 454.42 0.05 0.02 0.02

MCB cycle size 3 4 3.02 3.00 25,759 MAX VALUE 9,419.07 0.14 0.05 0.10

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.54	0.51	0.50	209.69	0.00	-281.68	0.01	0.02	4.84
Degree	28	48	40.28	41.00	16,674	MAX VALUE	1,527.92	4.00	0.10	2.74
Eccentricity	2	3	3.00	3.00	1,241	MAX VALUE	454.42	0.05	0.02	0.02
MCB cycle size	3	4	3.02	3.00	25,759	MAX VALUE	9,419.07	0.14	0.05	0.10

Minimal dual graph

Density: 0.92%
MCB compute time (ms): 1,549
MCB cycles: 375

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 2 6 3.81 4.00 1,576 MAX VALUE 542.15 0.91 0.24 1.22

Eccentricity 7 10 8.24 8.00 3,410 MAX VALUE 871.89 0.59 0.07 0.89

MCB cycle size 4 9 6.59 7.00 2,470 MAX VALUE 699.45 1.26 0.19 1.61

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	2	6	3.81	4.00	1,576	MAX VALUE	542.15	0.91	0.24	1.22
Eccentricity	7	10	8.24	8.00	3,410	MAX VALUE	871.89	0.59	0.07	0.89
MCB cycle size	4	9	6.59	7.00	2,470	MAX VALUE	699.45	1.26	0.19	1.61

Triangulated dual graph

Density: None%
Triangles: None

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

Clustering coefficient None None None None None None None None None None

Degree None None None None None None None None None None

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	None	None	None	None	None	None	None	None	None	None
Degree	None	None	None	None	None	None	None	None	None	None
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 9.84%

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

Clustering coefficient 0.54 1.00 0.83 0.80 342.35 0.00 -84.65 0.14 0.17 3.76

Degree 2 139 40.63 8.00 16,822 MAX VALUE 1,107.43 51.02 1.26 3.44

Eccentricity 3 5 3.77 4.00 1,559 MAX VALUE 544.60 0.53 0.14 0.79

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.54	1.00	0.83	0.80	342.35	0.00	-84.65	0.14	0.17	3.76
Degree	2	139	40.63	8.00	16,822	MAX VALUE	1,107.43	51.02	1.26	3.44
Eccentricity	3	5	3.77	4.00	1,559	MAX VALUE	544.60	0.53	0.14	0.79

Incidence graph

Density: 0.81%
MCB compute time (ms): 535
MCB cycles: 375
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-42-ext/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 2 25 3.65 2.00 1,656 MAX VALUE 407.71 5.38 1.47 0.50

Eccentricity 5 6 5.91 6.00 2,683 MAX VALUE 805.98 0.29 0.05 0.30

MCB cycle size 6 6 6.00 6.00 2,250 MAX VALUE 671.91 0.00 0.00 0.00

XCSP 2.1 Benchmarks