XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-11-414-200-36-ext
Number of variables: 40
Number of constraints: 414
Satisfiable: True
Timestamp: 2025-07-27 21:30:01
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 8.80 9.00 80,164 MAX VALUE 19,697.00 1.33 0.15 1.67

Relational linkage 0.27 0.73 0.56 0.55 245.82 0.00 -260.86 0.08 0.14 1.27

Tightness 0.11 0.34 0.20 0.20 82.74 0.00 -673.84 0.04 0.19 2.87

Tuples 80 108 96.82 97.00 40,082 MAX VALUE 1,892.69 4.50 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 15 28 20.70 21.00 828 MAX VALUE 120.81 2.88 0.14 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	8.80	9.00	80,164	MAX VALUE	19,697.00	1.33	0.15	1.67
Relational linkage	0.27	0.73	0.56	0.55	245.82	0.00	-260.86	0.08	0.14	1.27
Tightness	0.11	0.34	0.20	0.20	82.74	0.00	-673.84	0.04	0.19	2.87
Tuples	80	108	96.82	97.00	40,082	MAX VALUE	1,892.69	4.50	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	15	28	20.70	21.00	828	MAX VALUE	120.81	2.88	0.14	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: 10
Number of leaves: 6
Tree depth: 2
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/Tree1.json

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

Cluster constraints 71 253 138.80 128.00 1,388 1.28e+21 48.60 53.65 0.39 2.30

Variables per cluster 16 31 22.10 21.00 221 2.25e+13 30.75 4.57 0.21 2.03

Separator constraints 0 176 97.40 97.00 974 0 None 49.05 0.50 2.30

Separator variables 0 26 18.10 19.00 181 0 None 6.96 0.38 2.03

Clusters per var 1 10 5.53 6.00 221 2.00e+26 60.56 2.63 0.48 2.11

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	71	253	138.80	128.00	1,388	1.28e+21	48.60	53.65	0.39	2.30
Variables per cluster	16	31	22.10	21.00	221	2.25e+13	30.75	4.57	0.21	2.03
Separator constraints	0	176	97.40	97.00	974	0	None	49.05	0.50	2.30
Separator variables	0	26	18.10	19.00	181	0	None	6.96	0.38	2.03
Clusters per var	1	10	5.53	6.00	221	2.00e+26	60.56	2.63	0.48	2.11

Dual tree decomposition

Number of clusters: 38
Number of leaves: 20
Tree depth: 4
CIR: 0.03
Independent Cluster Pairs: 20
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/DualTree1.json

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

Cluster constraints 229 3,014 840.08 560.50 31,923 MAX VALUE 246.86 664.64 0.79 3.60

Variables per cluster 30 250 76.82 51.00 2,919 MAX VALUE 157.74 54.39 0.71 3.44

Separator constraints 0 1,648 621.08 468.50 23,601 0 None 384.39 0.62 3.60

Separator variables 0 183 65.92 47.00 2,505 0 None 41.19 0.62 3.37

Clusters per variable 1 9 7.05 8.00 2,919 MAX VALUE 771.10 2.19 0.31 1.74

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	229	3,014	840.08	560.50	31,923	MAX VALUE	246.86	664.64	0.79	3.60
Variables per cluster	30	250	76.82	51.00	2,919	MAX VALUE	157.74	54.39	0.71	3.44
Separator constraints	0	1,648	621.08	468.50	23,601	0	None	384.39	0.62	3.60
Separator variables	0	183	65.92	47.00	2,505	0	None	41.19	0.62	3.37
Clusters per variable	1	9	7.05	8.00	2,919	MAX VALUE	771.10	2.19	0.31	1.74

Primal graph

Density: 53.08%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,447
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/Primal1.json

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

Clustering coefficient 0.46 0.58 0.52 0.53 20.94 0.00 -25.94 0.03 0.05 3.58

Degree 15 28 20.70 21.00 828 MAX VALUE 120.81 2.88 0.14 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	0.58	0.52	0.53	20.94	0.00	-25.94	0.03	0.05	3.58
Degree	15	28	20.70	21.00	828	MAX VALUE	120.81	2.88	0.14	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: 82.82%
MCB compute time (ms): None
MCB cycles: None
Triangles: 6,285

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

Clustering coefficient 0.82 1.00 0.91 0.89 36.35 0.02 -3.89 0.05 0.06 3.27

Degree 15 39 32.30 35.00 1,292 MAX VALUE 137.82 6.79 0.21 2.34

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	0.82	1.00	0.91	0.89	36.35	0.02	-3.89	0.05	0.06	3.27
Degree	15	39	32.30	35.00	1,292	MAX VALUE	137.82	6.79	0.21	2.34
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: 9.73%
MCB compute time (ms): 4,143
MCB cycles: 9,228
Triangles: 55,592
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/Dual1.json

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

Clustering coefficient 0.49 0.55 0.51 0.50 209.47 0.00 -282.10 0.01 0.01 4.95

Degree 29 52 40.20 40.00 16,644 MAX VALUE 1,527.25 3.97 0.10 2.77

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

MCB cycle size 3 4 3.02 3.00 27,856 MAX VALUE 10,187.50 0.14 0.04 0.09

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.55	0.51	0.50	209.47	0.00	-282.10	0.01	0.01	4.95
Degree	29	52	40.20	40.00	16,644	MAX VALUE	1,527.25	3.97	0.10	2.77
Eccentricity	2	3	2.99	3.00	1,238	MAX VALUE	453.20	0.10	0.03	0.05
MCB cycle size	3	4	3.02	3.00	27,856	MAX VALUE	10,187.50	0.14	0.04	0.09

Minimal dual graph

Density: 0.92%
MCB compute time (ms): 1,705
MCB cycles: 375

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

Clustering coefficient 0.00 0.33 0.00 0.00 1.20 0.00 None 0.03 10.03 0.07

Degree 2 6 3.81 4.00 1,576 MAX VALUE 543.54 0.85 0.22 1.19

Eccentricity 7 11 8.65 9.00 3,583 MAX VALUE 891.76 0.78 0.09 1.17

MCB cycle size 3 10 6.46 7.00 2,424 MAX VALUE 692.35 1.23 0.19 1.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	1.20	0.00	None	0.03	10.03	0.07
Degree	2	6	3.81	4.00	1,576	MAX VALUE	543.54	0.85	0.22	1.19
Eccentricity	7	11	8.65	9.00	3,583	MAX VALUE	891.76	0.78	0.09	1.17
MCB cycle size	3	10	6.46	7.00	2,424	MAX VALUE	692.35	1.23	0.19	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: 9.17%

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

Clustering coefficient 0.52 1.00 0.82 0.79 339.79 0.00 -88.69 0.15 0.18 3.73

Degree 2 135 37.86 7.00 15,674 MAX VALUE 1,094.79 47.40 1.25 3.50

Eccentricity 3 5 4.05 4.00 1,678 MAX VALUE 575.09 0.57 0.14 0.86

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.52	1.00	0.82	0.79	339.79	0.00	-88.69	0.15	0.18	3.73
Degree	2	135	37.86	7.00	15,674	MAX VALUE	1,094.79	47.40	1.25	3.50
Eccentricity	3	5	4.05	4.00	1,678	MAX VALUE	575.09	0.57	0.14	0.86

Incidence graph

Density: 0.81%
MCB compute time (ms): 727
MCB cycles: 375
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-36-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 28 3.65 2.00 1,656 MAX VALUE 407.78 5.37 1.47 0.50

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