XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-11-414-200-46-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 79,968 MAX VALUE 19,671.80 1.33 0.15 1.68

Relational linkage 0.27 0.73 0.55 0.55 243.09 0.00 -266.64 0.08 0.15 1.31

Tightness 0.08 0.32 0.20 0.20 83.55 0.00 -669.70 0.04 0.18 2.88

Tuples 82 111 96.58 97.00 39,984 MAX VALUE 1,891.70 4.42 0.05 2.88

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

Value table constraints 16 27 20.70 21.00 828 MAX VALUE 120.86 2.69 0.13 2.29

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	79,968	MAX VALUE	19,671.80	1.33	0.15	1.68
Relational linkage	0.27	0.73	0.55	0.55	243.09	0.00	-266.64	0.08	0.15	1.31
Tightness	0.08	0.32	0.20	0.20	83.55	0.00	-669.70	0.04	0.18	2.88
Tuples	82	111	96.58	97.00	39,984	MAX VALUE	1,891.70	4.42	0.05	2.88
Values	11	11	11.00	11.00	440	MAX VALUE	95.92	0.00	0.00	0.00
Value table constraints	16	27	20.70	21.00	828	MAX VALUE	120.86	2.69	0.13	2.29
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: 12
Number of leaves: 5
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/Tree1.json

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

Cluster constraints 73 230 165.00 201.50 1,980 1.41e+26 60.21 62.13 0.38 2.37

Variables per cluster 17 29 24.33 27.50 292 3.22e+16 38.01 5.14 0.21 1.70

Separator constraints 0 208 130.50 144.00 1,566 0 None 71.25 0.55 2.48

Separator variables 0 28 21.00 23.00 252 0 None 8.03 0.38 1.91

Clusters per var 1 12 7.30 8.00 292 8.49e+30 71.22 3.41 0.47 2.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	73	230	165.00	201.50	1,980	1.41e+26	60.21	62.13	0.38	2.37
Variables per cluster	17	29	24.33	27.50	292	3.22e+16	38.01	5.14	0.21	1.70
Separator constraints	0	208	130.50	144.00	1,566	0	None	71.25	0.55	2.48
Separator variables	0	28	21.00	23.00	252	0	None	8.03	0.38	1.91
Clusters per var	1	12	7.30	8.00	292	8.49e+30	71.22	3.41	0.47	2.28

Dual tree decomposition

Number of clusters: 38
Number of leaves: 19
Tree depth: 4
CIR: 0.03
Independent Cluster Pairs: 18
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/DualTree1.json

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

Cluster constraints 259 3,065 828.74 559.50 31,492 MAX VALUE 246.75 643.83 0.78 3.60

Variables per cluster 32 250 76.29 51.50 2,899 MAX VALUE 157.63 53.70 0.70 3.42

Separator constraints 0 1,555 610.29 494.50 23,191 0 None 371.05 0.61 3.56

Separator variables 0 178 65.39 46.50 2,485 0 None 40.62 0.62 3.42

Clusters per variable 1 9 7.00 8.00 2,899 MAX VALUE 767.04 2.23 0.32 1.74

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	259	3,065	828.74	559.50	31,492	MAX VALUE	246.75	643.83	0.78	3.60
Variables per cluster	32	250	76.29	51.50	2,899	MAX VALUE	157.63	53.70	0.70	3.42
Separator constraints	0	1,555	610.29	494.50	23,191	0	None	371.05	0.61	3.56
Separator variables	0	178	65.39	46.50	2,485	0	None	40.62	0.62	3.42
Clusters per variable	1	9	7.00	8.00	2,899	MAX VALUE	767.04	2.23	0.32	1.74

Primal graph

Density: 53.08%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,459
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/Primal1.json

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

Clustering coefficient 0.47 0.58 0.53 0.53 21.10 0.00 -25.63 0.02 0.04 3.55

Degree 16 27 20.70 21.00 828 MAX VALUE 120.86 2.69 0.13 2.29

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	0.58	0.53	0.53	21.10	0.00	-25.63	0.02	0.04	3.55
Degree	16	27	20.70	21.00	828	MAX VALUE	120.86	2.69	0.13	2.29
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: 84.36%
MCB compute time (ms): None
MCB cycles: None
Triangles: 6,561

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

Clustering coefficient 0.84 1.00 0.92 0.92 36.64 0.03 -3.56 0.05 0.05 3.15

Degree 16 39 32.90 35.00 1,316 MAX VALUE 138.70 6.44 0.20 2.44

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	0.84	1.00	0.92	0.92	36.64	0.03	-3.56	0.05	0.05	3.15
Degree	16	39	32.90	35.00	1,316	MAX VALUE	138.70	6.44	0.20	2.44
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: 9.71%
MCB compute time (ms): 8,545
MCB cycles: 8,505
Triangles: 55,169
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/Dual1.json

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

Clustering coefficient 0.49 0.53 0.51 0.50 209.17 0.00 -282.67 0.01 0.01 4.83

Degree 31 50 40.10 40.00 16,602 MAX VALUE 1,526.40 3.75 0.09 2.72

Eccentricity 3 3 3.00 3.00 1,242 MAX VALUE 454.82 0.00 0.00 0.00

MCB cycle size 3 4 3.01 3.00 25,606 MAX VALUE 9,369.88 0.10 0.03 0.06

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.53	0.51	0.50	209.17	0.00	-282.67	0.01	0.01	4.83
Degree	31	50	40.10	40.00	16,602	MAX VALUE	1,526.40	3.75	0.09	2.72
Eccentricity	3	3	3.00	3.00	1,242	MAX VALUE	454.82	0.00	0.00	0.00
MCB cycle size	3	4	3.01	3.00	25,606	MAX VALUE	9,369.88	0.10	0.03	0.06

Minimal dual graph

Density: 0.92%
MCB compute time (ms): 1,446
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 542.84 0.89 0.23 1.21

Eccentricity 6 10 8.17 8.00 3,384 MAX VALUE 868.00 0.76 0.09 1.14

MCB cycle size 4 9 6.55 7.00 2,456 MAX VALUE 697.96 1.21 0.18 1.58

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	542.84	0.89	0.23	1.21
Eccentricity	6	10	8.17	8.00	3,384	MAX VALUE	868.00	0.76	0.09	1.14
MCB cycle size	4	9	6.55	7.00	2,456	MAX VALUE	697.96	1.21	0.18	1.58

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: 10.24%

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

Clustering coefficient 0.51 1.00 0.83 0.80 343.65 0.00 -82.87 0.14 0.17 3.78

Degree 2 140 42.30 9.00 17,514 MAX VALUE 1,118.87 52.71 1.25 3.46

Eccentricity 3 5 3.74 4.00 1,547 MAX VALUE 541.47 0.53 0.14 0.77

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.51	1.00	0.83	0.80	343.65	0.00	-82.87	0.14	0.17	3.78
Degree	2	140	42.30	9.00	17,514	MAX VALUE	1,118.87	52.71	1.25	3.46
Eccentricity	3	5	3.74	4.00	1,547	MAX VALUE	541.47	0.53	0.14	0.77

Incidence graph

Density: 0.81%
MCB compute time (ms): 720
MCB cycles: 375
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-46-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 407.83 5.36 1.47 0.50

Eccentricity 5 6 5.91 6.00 2,684 MAX VALUE 806.17 0.28 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