XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-16-250-350-49-ext
Number of variables: 40
Number of constraints: 250
Satisfiable: True
Timestamp: 2025-07-20 22:09:22
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 250

General features

Coarse blocks: 8,000
Value tables: 40

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

Arity 2 2 2.00 2.00 500 MAX VALUE 173.29 0.00 0.00 0.00

Coarse blocks size 3 16 10.37 10.00 82,928 MAX VALUE 18,559.80 1.92 0.19 2.07

Relational linkage 0.19 0.62 0.45 0.44 286.75 0.00 -523.41 0.07 0.17 1.58

Tightness 0.28 0.44 0.35 0.35 88.03 0.00 -261.89 0.03 0.09 3.38

Tuples 143 185 165.86 166.00 41,464 MAX VALUE 1,277.50 7.86 0.05 3.38

Values 16 16 16.00 16.00 640 MAX VALUE 110.90 0.00 0.00 0.00

Value table constraints 7 20 12.50 12.00 500 MAX VALUE 99.86 2.99 0.24 2.42

Value table partitions 16 16 16.00 16.00 640 MAX VALUE 110.90 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	500	MAX VALUE	173.29	0.00	0.00	0.00
Coarse blocks size	3	16	10.37	10.00	82,928	MAX VALUE	18,559.80	1.92	0.19	2.07
Relational linkage	0.19	0.62	0.45	0.44	286.75	0.00	-523.41	0.07	0.17	1.58
Tightness	0.28	0.44	0.35	0.35	88.03	0.00	-261.89	0.03	0.09	3.38
Tuples	143	185	165.86	166.00	41,464	MAX VALUE	1,277.50	7.86	0.05	3.38
Values	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00
Value table constraints	7	20	12.50	12.00	500	MAX VALUE	99.86	2.99	0.24	2.42
Value table partitions	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00

Tree decomposition

Number of clusters: 18
Number of leaves: 9
Tree depth: 4
CIR: 0.01
Independent Cluster Pairs: 1
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/Tree1.json

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

Cluster constraints 15 86 41.83 34.50 753 8.86e+27 64.35 23.06 0.55 2.74

Variables per cluster 8 23 14.39 13.50 259 2.29e+20 46.88 5.09 0.35 2.40

Separator constraints 0 66 27.94 19.00 503 0 None 20.90 0.75 2.66

Separator variables 0 21 12.17 11.00 219 0 None 5.50 0.45 2.40

Clusters per var 1 15 6.47 6.00 259 1.45e+26 60.24 4.38 0.68 2.35

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	15	86	41.83	34.50	753	8.86e+27	64.35	23.06	0.55	2.74
Variables per cluster	8	23	14.39	13.50	259	2.29e+20	46.88	5.09	0.35	2.40
Separator constraints	0	66	27.94	19.00	503	0	None	20.90	0.75	2.66
Separator variables	0	21	12.17	11.00	219	0	None	5.50	0.45	2.40
Clusters per var	1	15	6.47	6.00	259	1.45e+26	60.24	4.38	0.68	2.35

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.12
Independent Cluster Pairs: 80
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/DualTree1.json

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

Cluster constraints 64 878 275.79 209.00 10,480 MAX VALUE 204.65 208.33 0.76 3.60

Variables per cluster 16 130 43.45 31.50 1,651 MAX VALUE 136.25 30.05 0.69 3.40

Separator constraints 0 542 195.42 160.50 7,426 0 None 125.36 0.64 3.64

Separator variables 0 102 36.87 29.00 1,401 0 None 23.12 0.63 3.32

Clusters per variable 1 11 6.60 7.00 1,651 MAX VALUE 438.93 2.53 0.38 2.09

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	64	878	275.79	209.00	10,480	MAX VALUE	204.65	208.33	0.76	3.60
Variables per cluster	16	130	43.45	31.50	1,651	MAX VALUE	136.25	30.05	0.69	3.40
Separator constraints	0	542	195.42	160.50	7,426	0	None	125.36	0.64	3.64
Separator variables	0	102	36.87	29.00	1,401	0	None	23.12	0.63	3.32
Clusters per variable	1	11	6.60	7.00	1,651	MAX VALUE	438.93	2.53	0.38	2.09

Primal graph

Density: 32.05%
MCB compute time (ms): 6
MCB cycles: 216
Triangles: 331
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/Primal1.json

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

Clustering coefficient 0.22 0.45 0.33 0.33 13.32 0.00 -44.48 0.05 0.16 3.33

Degree 7 20 12.50 12.00 500 MAX VALUE 99.86 2.99 0.24 2.42

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.02 3.00 652 MAX VALUE 238.45 0.13 0.04 0.09

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.22	0.45	0.33	0.33	13.32	0.00	-44.48	0.05	0.16	3.33
Degree	7	20	12.50	12.00	500	MAX VALUE	99.86	2.99	0.24	2.42
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.02	3.00	652	MAX VALUE	238.45	0.13	0.04	0.09

Triangulated primal graph

Density: 60.51%
MCB compute time (ms): 9
MCB cycles: 475
Triangles: 3,266

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

Clustering coefficient 0.65 1.00 0.85 0.84 34.12 0.00 -6.68 0.11 0.13 3.19

Degree 7 36 23.60 27.00 944 MAX VALUE 121.93 9.42 0.40 2.88

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,425 MAX VALUE 521.84 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.65	1.00	0.85	0.84	34.12	0.00	-6.68	0.11	0.13	3.19
Degree	7	36	23.60	27.00	944	MAX VALUE	121.93	9.42	0.40	2.88
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,425	MAX VALUE	521.84	0.00	0.00	0.00

Dual graph

Density: 9.81%
MCB compute time (ms): 607
MCB cycles: 3,344
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/Dual1.json

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

Clustering coefficient 0.47 0.63 0.51 0.50 127.45 0.00 -168.67 0.02 0.05 4.72

Degree 15 35 24.43 24.00 6,108 MAX VALUE 795.53 3.99 0.16 2.77

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.05 3.00 10,197 MAX VALUE 3,721.23 0.22 0.07 0.20

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.63	0.51	0.50	127.45	0.00	-168.67	0.02	0.05	4.72
Degree	15	35	24.43	24.00	6,108	MAX VALUE	795.53	3.99	0.16	2.77
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.05	3.00	10,197	MAX VALUE	3,721.23	0.22	0.07	0.20

Minimal dual graph

Density: 1.48%
MCB compute time (ms): 179
MCB cycles: 211

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

Clustering coefficient 0.00 0.17 0.00 0.00 0.63 0.00 None 0.02 6.63 0.13

Degree 2 6 3.68 4.00 920 MAX VALUE 319.04 0.86 0.23 1.22

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.74 7.00 1,422 MAX VALUE 399.05 1.16 0.17 1.53

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.63	0.00	None	0.02	6.63	0.13
Degree	2	6	3.68	4.00	920	MAX VALUE	319.04	0.86	0.23	1.22
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.74	7.00	1,422	MAX VALUE	399.05	1.16	0.17	1.53

Triangulated dual graph

Density: 54.36%
Triangles: 729,006

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

Clustering coefficient 0.73 1.00 0.85 0.84 213.25 0.00 -40.65 0.07 0.09 4.87

Degree 15 203 135.36 160.00 33,840 MAX VALUE 1,185.41 58.62 0.43 4.12

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	0.73	1.00	0.85	0.84	213.25	0.00	-40.65	0.07	0.09	4.87
Degree	15	203	135.36	160.00	33,840	MAX VALUE	1,185.41	58.62	0.43	4.12
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 10.69%

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

Clustering coefficient 0.54 1.00 0.81 0.78 202.85 0.00 -56.50 0.15 0.18 3.47

Degree 2 85 26.62 7.00 6,656 MAX VALUE 612.79 31.39 1.18 3.16

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	0.54	1.00	0.81	0.78	202.85	0.00	-56.50	0.15	0.18	3.47
Degree	2	85	26.62	7.00	6,656	MAX VALUE	612.79	31.39	1.18	3.16
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.19%
MCB compute time (ms): 71
MCB cycles: 211
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-49-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 20 3.45 2.00 1,000 MAX VALUE 273.14 3.79 1.10 0.73

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.02 6.00 1,270 MAX VALUE 378.64 0.19 0.03 0.05

XCSP 2.1 Benchmarks