XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-25-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:27
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 180

General features

Coarse blocks: 9,000
Value tables: 40

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

Arity 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00

Coarse blocks size 4 21 12.54 13.00 112,838 MAX VALUE 22,571.60 2.48 0.20 2.33

Relational linkage 0.16 0.60 0.36 0.36 359.44 0.00 -1,039.33 0.06 0.17 1.86

Tightness 0.46 0.56 0.50 0.50 89.73 0.00 -125.44 0.02 0.04 3.69

Tuples 276 340 313.44 314.00 56,419 MAX VALUE 1,034.44 11.93 0.04 3.69

Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Value table constraints 4 15 9.00 9.00 360 2.91e+37 86.26 2.38 0.26 2.12

Value table partitions 25 25 25.00 25.00 1,000 MAX VALUE 128.75 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	360	MAX VALUE	124.77	0.00	0.00	0.00
Coarse blocks size	4	21	12.54	13.00	112,838	MAX VALUE	22,571.60	2.48	0.20	2.33
Relational linkage	0.16	0.60	0.36	0.36	359.44	0.00	-1,039.33	0.06	0.17	1.86
Tightness	0.46	0.56	0.50	0.50	89.73	0.00	-125.44	0.02	0.04	3.69
Tuples	276	340	313.44	314.00	56,419	MAX VALUE	1,034.44	11.93	0.04	3.69
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	15	9.00	9.00	360	2.91e+37	86.26	2.38	0.26	2.12
Value table partitions	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00

Tree decomposition

Number of clusters: 20
Number of leaves: 9
Tree depth: 4
CIR: 0.09
Independent Cluster Pairs: 16
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/Tree1.json

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

Cluster constraints 5 58 23.55 19.00 471 1.15e+25 57.70 17.06 0.72 2.72

Variables per cluster 5 21 11.75 10.00 235 3.19e+20 47.21 5.27 0.45 2.30

Separator constraints 0 50 14.55 9.00 291 0 None 15.27 1.05 2.53

Separator variables 0 20 9.75 8.00 195 0 None 5.32 0.55 2.37

Clusters per var 1 13 5.88 6.00 235 4.22e+24 56.70 4.04 0.69 2.34

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	58	23.55	19.00	471	1.15e+25	57.70	17.06	0.72	2.72
Variables per cluster	5	21	11.75	10.00	235	3.19e+20	47.21	5.27	0.45	2.30
Separator constraints	0	50	14.55	9.00	291	0	None	15.27	1.05	2.53
Separator variables	0	20	9.75	8.00	195	0	None	5.32	0.55	2.37
Clusters per var	1	13	5.88	6.00	235	4.22e+24	56.70	4.04	0.69	2.34

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 133
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/DualTree1.json

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

Cluster constraints 22 398 127.66 103.50 4,851 MAX VALUE 175.67 88.91 0.70 3.49

Variables per cluster 9 89 29.39 21.00 1,117 MAX VALUE 121.81 19.35 0.66 3.28

Separator constraints 0 225 86.79 83.50 3,298 0 None 53.08 0.61 3.48

Separator variables 0 68 24.66 19.50 937 0 None 14.72 0.60 3.24

Clusters per variable 1 10 6.21 7.00 1,117 MAX VALUE 300.42 2.59 0.42 2.03

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	22	398	127.66	103.50	4,851	MAX VALUE	175.67	88.91	0.70	3.49
Variables per cluster	9	89	29.39	21.00	1,117	MAX VALUE	121.81	19.35	0.66	3.28
Separator constraints	0	225	86.79	83.50	3,298	0	None	53.08	0.61	3.48
Separator variables	0	68	24.66	19.50	937	0	None	14.72	0.60	3.24
Clusters per variable	1	10	6.21	7.00	1,117	MAX VALUE	300.42	2.59	0.42	2.03

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 168
Triangles: 110
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/Primal1.json

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

Clustering coefficient 0.07 0.47 0.22 0.20 8.77 0.00 -63.82 0.09 0.40 3.25

Degree 4 15 9.00 9.00 360 2.91e+37 86.26 2.38 0.26 2.12

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.39 3.00 570 MAX VALUE 203.55 0.49 0.14 0.67

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.07	0.47	0.22	0.20	8.77	0.00	-63.82	0.09	0.40	3.25
Degree	4	15	9.00	9.00	360	2.91e+37	86.26	2.38	0.26	2.12
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.39	3.00	570	MAX VALUE	203.55	0.49	0.14	0.67

Triangulated primal graph

Density: 51.92%
MCB compute time (ms): 10
MCB cycles: 372
Triangles: 2,466

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

Clustering coefficient 0.65 1.00 0.84 0.82 33.62 0.00 -7.30 0.11 0.13 3.19

Degree 4 32 20.25 24.50 810 MAX VALUE 113.44 9.60 0.47 2.78

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,116 MAX VALUE 408.68 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	0.84	0.82	33.62	0.00	-7.30	0.11	0.13	3.19
Degree	4	32	20.25	24.50	810	MAX VALUE	113.44	9.60	0.47	2.78
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,116	MAX VALUE	408.68	0.00	0.00	0.00

Dual graph

Density: 9.64%
MCB compute time (ms): 371
MCB cycles: 1,628
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/Dual1.json

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

Clustering coefficient 0.44 0.64 0.50 0.49 90.49 0.00 -124.17 0.03 0.07 4.02

Degree 8 25 17.26 18.00 3,106 MAX VALUE 509.56 3.05 0.18 2.46

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.18 3.00 5,179 MAX VALUE 1,872.70 0.40 0.13 0.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.64	0.50	0.49	90.49	0.00	-124.17	0.03	0.07	4.02
Degree	8	25	17.26	18.00	3,106	MAX VALUE	509.56	3.05	0.18	2.46
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.18	3.00	5,179	MAX VALUE	1,872.70	0.40	0.13	0.49

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 82
MCB cycles: 141

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

Clustering coefficient 0.00 0.17 0.00 0.00 0.50 0.00 None 0.02 7.68 0.08

Degree 2 5 3.56 3.00 640 MAX VALUE 223.84 0.79 0.22 1.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.73 7.00 949 MAX VALUE 266.57 1.14 0.17 1.51

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.50	0.00	None	0.02	7.68	0.08
Degree	2	5	3.56	3.00	640	MAX VALUE	223.84	0.79	0.22	1.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.73	7.00	949	MAX VALUE	266.57	1.14	0.17	1.51

Triangulated dual graph

Density: 48.22%
Triangles: 213,805

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

Clustering coefficient 0.71 1.00 0.84 0.81 150.91 0.00 -32.56 0.08 0.10 4.55

Degree 8 131 86.31 97.50 15,536 MAX VALUE 767.29 41.28 0.48 3.75

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	0.71	1.00	0.84	0.81	150.91	0.00	-32.56	0.08	0.10	4.55
Degree	8	131	86.31	97.50	15,536	MAX VALUE	767.29	41.28	0.48	3.75
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.50%

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

Clustering coefficient 0.48 1.00 0.80 0.75 143.78 0.00 -43.90 0.16 0.20 3.26

Degree 2 67 20.58 7.00 3,704 MAX VALUE 416.87 22.81 1.11 3.07

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	0.48	1.00	0.80	0.75	143.78	0.00	-43.90	0.16	0.20	3.26
Degree	2	67	20.58	7.00	3,704	MAX VALUE	416.87	22.81	1.11	3.07
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 41
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-25-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 15 3.27 2.00 720 MAX VALUE 211.03 2.88 0.88 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.55 6.00 924 MAX VALUE 263.86 0.89 0.14 0.59

XCSP 2.1 Benchmarks