XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-54-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:28
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 2 21 12.54 13.00 112,852 MAX VALUE 22,569.00 2.50 0.20 2.33

Relational linkage 0.08 0.52 0.36 0.36 356.04 0.00 -1,047.93 0.06 0.17 1.80

Tightness 0.45 0.55 0.50 0.50 89.72 0.00 -125.46 0.02 0.04 3.69

Tuples 284 346 313.48 313.00 56,426 MAX VALUE 1,034.47 11.64 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 5 15 9.00 9.50 360 4.28e+37 86.65 2.26 0.25 1.91

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	2	21	12.54	13.00	112,852	MAX VALUE	22,569.00	2.50	0.20	2.33
Relational linkage	0.08	0.52	0.36	0.36	356.04	0.00	-1,047.93	0.06	0.17	1.80
Tightness	0.45	0.55	0.50	0.50	89.72	0.00	-125.46	0.02	0.04	3.69
Tuples	284	346	313.48	313.00	56,426	MAX VALUE	1,034.47	11.64	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	5	15	9.00	9.50	360	4.28e+37	86.65	2.26	0.25	1.91
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: 10
Tree depth: 4
CIR: 0.08
Independent Cluster Pairs: 14
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/Tree1.json

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

Cluster constraints 7 57 24.40 16.50 488 3.50e+25 58.82 17.62 0.72 2.58

Variables per cluster 6 21 12.25 9.50 245 9.28e+20 48.28 5.32 0.43 2.14

Separator constraints 0 51 15.40 6.50 308 0 None 16.77 1.09 2.62

Separator variables 0 20 10.25 8.00 205 0 None 5.46 0.53 2.25

Clusters per var 1 13 6.12 7.00 245 1.73e+25 58.11 4.04 0.66 2.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	57	24.40	16.50	488	3.50e+25	58.82	17.62	0.72	2.58
Variables per cluster	6	21	12.25	9.50	245	9.28e+20	48.28	5.32	0.43	2.14
Separator constraints	0	51	15.40	6.50	308	0	None	16.77	1.09	2.62
Separator variables	0	20	10.25	8.00	205	0	None	5.46	0.53	2.25
Clusters per var	1	13	6.12	7.00	245	1.73e+25	58.11	4.04	0.66	2.28

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.18
Independent Cluster Pairs: 122
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/DualTree1.json

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

Cluster constraints 26 336 121.05 92.00 4,600 MAX VALUE 174.64 80.33 0.66 3.53

Variables per cluster 10 84 29.18 21.50 1,109 MAX VALUE 121.84 18.92 0.65 3.17

Separator constraints 0 194 80.47 73.00 3,058 0 None 47.95 0.60 3.46

Separator variables 0 65 24.45 19.50 929 0 None 14.52 0.59 3.12

Clusters per variable 1 11 6.16 7.00 1,109 MAX VALUE 296.65 2.77 0.45 2.20

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	26	336	121.05	92.00	4,600	MAX VALUE	174.64	80.33	0.66	3.53
Variables per cluster	10	84	29.18	21.50	1,109	MAX VALUE	121.84	18.92	0.65	3.17
Separator constraints	0	194	80.47	73.00	3,058	0	None	47.95	0.60	3.46
Separator variables	0	65	24.45	19.50	929	0	None	14.52	0.59	3.12
Clusters per variable	1	11	6.16	7.00	1,109	MAX VALUE	296.65	2.77	0.45	2.20

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 148
Triangles: 103
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/Primal1.json

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

Clustering coefficient 0.07 0.50 0.20 0.20 7.99 0.00 -67.91 0.08 0.41 3.00

Degree 5 15 9.00 9.50 360 4.28e+37 86.65 2.26 0.25 1.91

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.36 3.00 497 MAX VALUE 177.84 0.48 0.14 0.65

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.07	0.50	0.20	0.20	7.99	0.00	-67.91	0.08	0.41	3.00
Degree	5	15	9.00	9.50	360	4.28e+37	86.65	2.26	0.25	1.91
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.36	3.00	497	MAX VALUE	177.84	0.48	0.14	0.65

Triangulated primal graph

Density: 53.21%
MCB compute time (ms): 9
MCB cycles: 399
Triangles: 2,576

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

Clustering coefficient 0.66 1.00 0.84 0.81 33.65 0.00 -7.24 0.11 0.13 3.11

Degree 5 32 20.75 26.00 830 MAX VALUE 114.96 9.55 0.46 2.69

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,197 MAX VALUE 438.35 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.66	1.00	0.84	0.81	33.65	0.00	-7.24	0.11	0.13	3.11
Degree	5	32	20.75	26.00	830	MAX VALUE	114.96	9.55	0.46	2.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,197	MAX VALUE	438.35	0.00	0.00	0.00

Dual graph

Density: 9.57%
MCB compute time (ms): 483
MCB cycles: 1,566
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/Dual1.json

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

Clustering coefficient 0.45 0.58 0.50 0.49 89.79 0.00 -125.41 0.03 0.05 3.90

Degree 9 28 17.13 17.00 3,084 MAX VALUE 507.94 3.34 0.19 2.53

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.16 3.00 4,948 MAX VALUE 1,791.96 0.38 0.12 0.45

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.58	0.50	0.49	89.79	0.00	-125.41	0.03	0.05	3.90
Degree	9	28	17.13	17.00	3,084	MAX VALUE	507.94	3.34	0.19	2.53
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.16	3.00	4,948	MAX VALUE	1,791.96	0.38	0.12	0.45

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 75
MCB cycles: 141

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

Clustering coefficient 0.00 0.33 0.01 0.00 1.20 0.00 None 0.04 6.02 0.18

Degree 2 5 3.56 3.00 640 MAX VALUE 224.22 0.75 0.21 1.11

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.74 7.00 950 MAX VALUE 266.22 1.22 0.18 1.50

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	1.20	0.00	None	0.04	6.02	0.18
Degree	2	5	3.56	3.00	640	MAX VALUE	224.22	0.75	0.21	1.11
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.74	7.00	950	MAX VALUE	266.22	1.22	0.18	1.50

Triangulated dual graph

Density: 46.77%
Triangles: 200,747

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

Clustering coefficient 0.72 1.00 0.84 0.81 150.46 0.00 -33.22 0.09 0.10 4.65

Degree 9 131 83.72 102.00 15,070 MAX VALUE 760.60 41.07 0.49 4.03

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	0.72	1.00	0.84	0.81	150.46	0.00	-33.22	0.09	0.10	4.65
Degree	9	131	83.72	102.00	15,070	MAX VALUE	760.60	41.07	0.49	4.03
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 0.50 1.00 0.79 0.73 142.20 0.00 -45.97 0.16 0.20 3.38

Degree 2 62 20.59 7.00 3,706 MAX VALUE 420.21 22.51 1.09 3.09

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	0.50	1.00	0.79	0.73	142.20	0.00	-45.97	0.16	0.20	3.38
Degree	2	62	20.59	7.00	3,706	MAX VALUE	420.21	22.51	1.09	3.09
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 47
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-54-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 211.41 2.87 0.88 0.82

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.65 6.00 938 MAX VALUE 265.87 0.94 0.14 0.63

XCSP 2.1 Benchmarks