XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-11-414-200-56-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 8.78 9.00 80,000 MAX VALUE 19,677.70 1.32 0.15 1.67

Relational linkage 0.27 0.73 0.55 0.55 243.64 0.00 -265.63 0.08 0.15 1.31

Tightness 0.12 0.35 0.20 0.21 83.42 0.00 -670.16 0.04 0.18 2.85

Tuples 79 107 96.62 96.00 40,000 MAX VALUE 1,891.87 4.39 0.05 2.85

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

Value table constraints 15 27 20.70 20.50 828 MAX VALUE 120.77 3.03 0.15 2.32

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	8.78	9.00	80,000	MAX VALUE	19,677.70	1.32	0.15	1.67
Relational linkage	0.27	0.73	0.55	0.55	243.64	0.00	-265.63	0.08	0.15	1.31
Tightness	0.12	0.35	0.20	0.21	83.42	0.00	-670.16	0.04	0.18	2.85
Tuples	79	107	96.62	96.00	40,000	MAX VALUE	1,891.87	4.39	0.05	2.85
Values	11	11	11.00	11.00	440	MAX VALUE	95.92	0.00	0.00	0.00
Value table constraints	15	27	20.70	20.50	828	MAX VALUE	120.77	3.03	0.15	2.32
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: 7
Tree depth: 2
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/Tree1.json

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

Cluster constraints 63 239 142.18 123.00 1,564 1.71e+23 53.50 60.51 0.43 2.40

Variables per cluster 16 30 22.27 21.00 245 5.08e+14 33.86 5.05 0.23 2.02

Separator constraints 0 221 104.55 98.00 1,150 0 None 61.70 0.59 2.40

Separator variables 0 29 18.64 19.00 205 0 None 7.36 0.40 2.15

Clusters per var 1 11 6.12 7.00 245 3.98e+27 63.55 2.98 0.49 2.11

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	63	239	142.18	123.00	1,564	1.71e+23	53.50	60.51	0.43	2.40
Variables per cluster	16	30	22.27	21.00	245	5.08e+14	33.86	5.05	0.23	2.02
Separator constraints	0	221	104.55	98.00	1,150	0	None	61.70	0.59	2.40
Separator variables	0	29	18.64	19.00	205	0	None	7.36	0.40	2.15
Clusters per var	1	11	6.12	7.00	245	3.98e+27	63.55	2.98	0.49	2.11

Dual tree decomposition

Number of clusters: 38
Number of leaves: 20
Tree depth: 5
CIR: 0.03
Independent Cluster Pairs: 22
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/DualTree1.json

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

Cluster constraints 229 2,884 839.74 570.00 31,910 MAX VALUE 246.84 656.45 0.78 3.48

Variables per cluster 30 243 76.76 50.50 2,917 MAX VALUE 157.68 54.50 0.71 3.43

Separator constraints 0 1,639 620.29 489.00 23,571 0 None 381.68 0.62 3.48

Separator variables 0 187 65.87 47.50 2,503 0 None 41.52 0.63 3.43

Clusters per variable 1 10 7.05 8.00 2,917 MAX VALUE 770.13 2.24 0.32 1.90

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	229	2,884	839.74	570.00	31,910	MAX VALUE	246.84	656.45	0.78	3.48
Variables per cluster	30	243	76.76	50.50	2,917	MAX VALUE	157.68	54.50	0.71	3.43
Separator constraints	0	1,639	620.29	489.00	23,571	0	None	381.68	0.62	3.48
Separator variables	0	187	65.87	47.50	2,503	0	None	41.52	0.63	3.43
Clusters per variable	1	10	7.05	8.00	2,917	MAX VALUE	770.13	2.24	0.32	1.90

Primal graph

Density: 53.08%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,454
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/Primal1.json

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

Clustering coefficient 0.46 0.59 0.52 0.52 20.96 0.00 -25.94 0.03 0.06 3.48

Degree 15 27 20.70 20.50 828 MAX VALUE 120.77 3.03 0.15 2.32

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	0.46	0.59	0.52	0.52	20.96	0.00	-25.94	0.03	0.06	3.48
Degree	15	27	20.70	20.50	828	MAX VALUE	120.77	3.03	0.15	2.32
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: 82.05%
MCB compute time (ms): None
MCB cycles: None
Triangles: 6,166

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

Clustering coefficient 0.81 1.00 0.91 0.90 36.28 0.02 -3.98 0.05 0.06 3.16

Degree 15 39 32.00 35.00 1,280 MAX VALUE 137.34 7.01 0.22 2.39

Eccentricity 1 2 1.98 2.00 79 5.50e+11 27.03 0.16 0.08 0.12

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	0.81	1.00	0.91	0.90	36.28	0.02	-3.98	0.05	0.06	3.16
Degree	15	39	32.00	35.00	1,280	MAX VALUE	137.34	7.01	0.22	2.39
Eccentricity	1	2	1.98	2.00	79	5.50e+11	27.03	0.16	0.08	0.12
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 9.75%
MCB compute time (ms): 7,971
MCB cycles: 8,452
Triangles: 55,912
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/Dual1.json

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

Clustering coefficient 0.49 0.54 0.51 0.50 209.73 0.00 -281.59 0.01 0.02 5.00

Degree 29 51 40.28 40.00 16,678 MAX VALUE 1,527.96 4.08 0.10 2.79

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

MCB cycle size 3 4 3.01 3.00 25,412 MAX VALUE 9,301.58 0.08 0.03 0.04

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.54	0.51	0.50	209.73	0.00	-281.59	0.01	0.02	5.00
Degree	29	51	40.28	40.00	16,678	MAX VALUE	1,527.96	4.08	0.10	2.79
Eccentricity	2	3	3.00	3.00	1,241	MAX VALUE	454.42	0.05	0.02	0.02
MCB cycle size	3	4	3.01	3.00	25,412	MAX VALUE	9,301.58	0.08	0.03	0.04

Minimal dual graph

Density: 0.92%
MCB compute time (ms): 1,783
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 542.89 0.88 0.23 1.20

Eccentricity 6 10 8.16 8.00 3,379 MAX VALUE 867.87 0.64 0.08 0.98

MCB cycle size 4 10 6.60 7.00 2,476 MAX VALUE 700.75 1.24 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	542.89	0.88	0.23	1.20
Eccentricity	6	10	8.16	8.00	3,379	MAX VALUE	867.87	0.64	0.08	0.98
MCB cycle size	4	10	6.60	7.00	2,476	MAX VALUE	700.75	1.24	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: 9.85%

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

Clustering coefficient 0.54 1.00 0.83 0.80 343.05 0.00 -83.90 0.14 0.17 3.76

Degree 2 139 40.67 8.50 16,838 MAX VALUE 1,107.83 51.04 1.25 3.48

Eccentricity 3 5 3.78 4.00 1,563 MAX VALUE 545.95 0.52 0.14 0.76

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.54	1.00	0.83	0.80	343.05	0.00	-83.90	0.14	0.17	3.76
Degree	2	139	40.67	8.50	16,838	MAX VALUE	1,107.83	51.04	1.25	3.48
Eccentricity	3	5	3.78	4.00	1,563	MAX VALUE	545.95	0.52	0.14	0.76

Incidence graph

Density: 0.81%
MCB compute time (ms): 668
MCB cycles: 375
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-56-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 27 3.65 2.00 1,656 MAX VALUE 407.73 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