XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-11-414-200-67-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 8.77 9.00 79,832 MAX VALUE 19,658.60 1.32 0.15 1.67

Relational linkage 0.27 0.73 0.56 0.55 244.73 0.00 -262.86 0.08 0.14 1.26

Tightness 0.09 0.32 0.20 0.20 84.12 0.00 -666.69 0.04 0.18 2.87

Tuples 82 110 96.42 97.00 39,916 MAX VALUE 1,891.00 4.38 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 12 27 20.70 21.00 828 MAX VALUE 120.65 3.31 0.16 2.47

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	8.77	9.00	79,832	MAX VALUE	19,658.60	1.32	0.15	1.67
Relational linkage	0.27	0.73	0.56	0.55	244.73	0.00	-262.86	0.08	0.14	1.26
Tightness	0.09	0.32	0.20	0.20	84.12	0.00	-666.69	0.04	0.18	2.87
Tuples	82	110	96.42	97.00	39,916	MAX VALUE	1,891.00	4.38	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	12	27	20.70	21.00	828	MAX VALUE	120.65	3.31	0.16	2.47
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: 10
Number of leaves: 6
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/Tree1.json

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

Cluster constraints 52 267 149.00 112.00 1,490 1.22e+21 48.55 78.82 0.53 2.16

Variables per cluster 13 31 22.20 20.00 222 1.92e+13 30.59 6.32 0.28 1.89

Separator constraints 0 249 107.60 83.00 1,076 0 None 76.66 0.71 2.16

Separator variables 0 30 18.20 18.00 182 0 None 8.26 0.45 2.03

Clusters per var 1 9 5.55 6.00 222 5.06e+26 61.49 2.42 0.44 1.96

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	52	267	149.00	112.00	1,490	1.22e+21	48.55	78.82	0.53	2.16
Variables per cluster	13	31	22.20	20.00	222	1.92e+13	30.59	6.32	0.28	1.89
Separator constraints	0	249	107.60	83.00	1,076	0	None	76.66	0.71	2.16
Separator variables	0	30	18.20	18.00	182	0	None	8.26	0.45	2.03
Clusters per var	1	9	5.55	6.00	222	5.06e+26	61.49	2.42	0.44	1.96

Dual tree decomposition

Number of clusters: 38
Number of leaves: 19
Tree depth: 5
CIR: 0.02
Independent Cluster Pairs: 16
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/DualTree1.json

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

Cluster constraints 161 2,993 841.53 567.00 31,978 MAX VALUE 246.47 682.25 0.81 3.60

Variables per cluster 25 243 76.42 51.00 2,904 MAX VALUE 157.42 54.78 0.72 3.39

Separator constraints 0 1,797 621.13 503.00 23,603 0 None 408.44 0.66 3.60

Separator variables 0 191 65.53 47.50 2,490 0 None 41.84 0.64 3.39

Clusters per variable 1 10 7.01 8.00 2,904 MAX VALUE 767.67 2.24 0.32 1.77

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	161	2,993	841.53	567.00	31,978	MAX VALUE	246.47	682.25	0.81	3.60
Variables per cluster	25	243	76.42	51.00	2,904	MAX VALUE	157.42	54.78	0.72	3.39
Separator constraints	0	1,797	621.13	503.00	23,603	0	None	408.44	0.66	3.60
Separator variables	0	191	65.53	47.50	2,490	0	None	41.84	0.64	3.39
Clusters per variable	1	10	7.01	8.00	2,904	MAX VALUE	767.67	2.24	0.32	1.77

Primal graph

Density: 53.08%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,506
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/Primal1.json

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

Clustering coefficient 0.47 0.61 0.54 0.54 21.62 0.00 -24.68 0.03 0.05 3.69

Degree 12 27 20.70 21.00 828 MAX VALUE 120.65 3.31 0.16 2.47

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	0.47	0.61	0.54	0.54	21.62	0.00	-24.68	0.03	0.05	3.69
Degree	12	27	20.70	21.00	828	MAX VALUE	120.65	3.31	0.16	2.47
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: 82.95%
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 0.84 1.00 0.92 0.91 36.66 0.03 -3.53 0.05 0.05 3.20

Degree 12 38 32.35 35.00 1,294 MAX VALUE 137.68 7.07 0.22 2.20

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	0.84	1.00	0.92	0.91	36.66	0.03	-3.53	0.05	0.05	3.20
Degree	12	38	32.35	35.00	1,294	MAX VALUE	137.68	7.07	0.22	2.20
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

Dual graph

Density: 9.80%
MCB compute time (ms): 8,588
MCB cycles: 8,289
Triangles: 56,585
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/Dual1.json

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

Clustering coefficient 0.49 0.58 0.51 0.50 210.25 0.00 -280.61 0.01 0.02 5.04

Degree 24 52 40.46 40.00 16,750 MAX VALUE 1,529.38 4.41 0.11 2.88

Eccentricity 2 3 2.99 3.00 1,238 MAX VALUE 453.20 0.10 0.03 0.05

MCB cycle size 3 4 3.00 3.00 24,885 MAX VALUE 9,111.58 0.05 0.02 0.02

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.58	0.51	0.50	210.25	0.00	-280.61	0.01	0.02	5.04
Degree	24	52	40.46	40.00	16,750	MAX VALUE	1,529.38	4.41	0.11	2.88
Eccentricity	2	3	2.99	3.00	1,238	MAX VALUE	453.20	0.10	0.03	0.05
MCB cycle size	3	4	3.00	3.00	24,885	MAX VALUE	9,111.58	0.05	0.02	0.02

Minimal dual graph

Density: 0.92%
MCB compute time (ms): 1,848
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 543.11 0.87 0.23 1.20

Eccentricity 6 9 7.93 8.00 3,283 MAX VALUE 855.80 0.66 0.08 0.99

MCB cycle size 4 9 6.72 7.00 2,519 MAX VALUE 708.22 1.16 0.17 1.55

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	543.11	0.87	0.23	1.20
Eccentricity	6	9	7.93	8.00	3,283	MAX VALUE	855.80	0.66	0.08	0.99
MCB cycle size	4	9	6.72	7.00	2,519	MAX VALUE	708.22	1.16	0.17	1.55

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: 10.52%

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

Clustering coefficient 0.54 1.00 0.83 0.80 344.31 0.00 -81.69 0.13 0.16 3.81

Degree 2 144 43.43 9.00 17,982 MAX VALUE 1,127.31 53.91 1.24 3.44

Eccentricity 3 6 4.26 4.00 1,762 MAX VALUE 595.11 0.62 0.14 0.93

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.54	1.00	0.83	0.80	344.31	0.00	-81.69	0.13	0.16	3.81
Degree	2	144	43.43	9.00	17,982	MAX VALUE	1,127.31	53.91	1.24	3.44
Eccentricity	3	6	4.26	4.00	1,762	MAX VALUE	595.11	0.62	0.14	0.93

Incidence graph

Density: 0.81%
MCB compute time (ms): 654
MCB cycles: 375
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-67-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 407.61 5.39 1.48 0.52

Eccentricity 5 6 5.90 6.00 2,680 MAX VALUE 805.44 0.30 0.05 0.32

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