XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-80-103-800-56-ext
Number of variables: 40
Number of constraints: 103
Satisfiable: True
Timestamp: 2025-07-20 22:09:37
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 103

General features

Coarse blocks: 16,400
Value tables: 39

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

Arity 2 2 2.00 2.00 206 1.01e+31 71.39 0.00 0.00 0.00

Coarse blocks size 4 31 15.94 16.00 261,380 MAX VALUE 44,970.70 3.57 0.22 2.69

Relational linkage 0.05 0.26 0.15 0.15 466.86 0.00 -5,995.18 0.03 0.20 2.31

Tightness 0.79 0.81 0.80 0.80 82.48 0.00 -22.88 0.00 0.01 4.20

Tuples 1,184 1,355 1,274.98 1,275.00 131,323 MAX VALUE 736.49 31.45 0.02 4.20

Values 80 80 80.00 80.00 3,200 MAX VALUE 175.28 0.00 0.00 0.00

Value table constraints 2 11 5.26 4.00 205 4.10e+26 61.28 2.19 0.42 1.94

Value table partitions 80 80 80.00 80.00 3,120 MAX VALUE 170.90 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	206	1.01e+31	71.39	0.00	0.00	0.00
Coarse blocks size	4	31	15.94	16.00	261,380	MAX VALUE	44,970.70	3.57	0.22	2.69
Relational linkage	0.05	0.26	0.15	0.15	466.86	0.00	-5,995.18	0.03	0.20	2.31
Tightness	0.79	0.81	0.80	0.80	82.48	0.00	-22.88	0.00	0.01	4.20
Tuples	1,184	1,355	1,274.98	1,275.00	131,323	MAX VALUE	736.49	31.45	0.02	4.20
Values	80	80	80.00	80.00	3,200	MAX VALUE	175.28	0.00	0.00	0.00
Value table constraints	2	11	5.26	4.00	205	4.10e+26	61.28	2.19	0.42	1.94
Value table partitions	80	80	80.00	80.00	3,120	MAX VALUE	170.90	0.00	0.00	0.00

Tree decomposition

Number of clusters: 28
Number of leaves: 14
Tree depth: 4
CIR: 0.41
Independent Cluster Pairs: 145
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/Tree1.json

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

Cluster constraints 1 19 6.54 5.00 183 1.58e+20 46.51 4.58 0.70 2.28

Variables per cluster 2 13 6.21 5.00 174 8.81e+20 48.23 2.94 0.47 2.18

Separator constraints 0 16 2.86 1.00 80 0 None 3.93 1.38 1.86

Separator variables 0 12 4.79 4.00 134 0 None 2.79 0.58 2.23

Clusters per var 1 13 4.35 2.00 174 2.06e+18 42.17 3.70 0.85 1.99

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	19	6.54	5.00	183	1.58e+20	46.51	4.58	0.70	2.28
Variables per cluster	2	13	6.21	5.00	174	8.81e+20	48.23	2.94	0.47	2.18
Separator constraints	0	16	2.86	1.00	80	0	None	3.93	1.38	1.86
Separator variables	0	12	4.79	4.00	134	0	None	2.79	0.58	2.23
Clusters per var	1	13	4.35	2.00	174	2.06e+18	42.17	3.70	0.85	1.99

Dual tree decomposition

Number of clusters: 38
Number of leaves: 12
Tree depth: 6
CIR: 0.42
Independent Cluster Pairs: 280
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/DualTree1.json

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

Cluster constraints 6 91 32.58 24.50 1,238 MAX VALUE 121.87 23.36 0.72 3.30

Variables per cluster 4 37 14.03 11.50 533 MAX VALUE 93.99 8.73 0.62 2.80

Separator constraints 0 47 18.63 15.50 708 0 None 13.86 0.74 3.32

Separator variables 0 29 11.32 10.00 430 0 None 6.83 0.60 2.78

Clusters per variable 1 11 5.17 6.00 533 MAX VALUE 147.80 2.81 0.54 2.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	91	32.58	24.50	1,238	MAX VALUE	121.87	23.36	0.72	3.30
Variables per cluster	4	37	14.03	11.50	533	MAX VALUE	93.99	8.73	0.62	2.80
Separator constraints	0	47	18.63	15.50	708	0	None	13.86	0.74	3.32
Separator variables	0	29	11.32	10.00	430	0	None	6.83	0.60	2.78
Clusters per variable	1	11	5.17	6.00	533	MAX VALUE	147.80	2.81	0.54	2.26

Primal graph

Density: 13.21%
MCB compute time (ms): 2
MCB cycles: 65
Triangles: 25
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 None 0.17 None None None None None 2.51

Degree 1 11 5.15 4.00 206 4.10e+26 61.28 2.26 0.44 2.01

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.72 4.00 242 5.21e+36 84.54 0.62 0.17 0.92

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	None	0.17	None	None	None	None	None	2.51
Degree	1	11	5.15	4.00	206	4.10e+26	61.28	2.26	0.44	2.01
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.72	4.00	242	5.21e+36	84.54	0.62	0.17	0.92

Triangulated primal graph

Density: 27.18%
MCB compute time (ms): 3
MCB cycles: 173
Triangles: 649

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

Clustering coefficient 0.50 1.00 None 0.73 None None None None None 2.95

Degree 1 24 10.60 6.50 424 2.85e+35 81.64 7.51 0.71 2.59

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 519 MAX VALUE 190.06 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.50	1.00	None	0.73	None	None	None	None	None	2.95
Degree	1	24	10.60	6.50	424	2.85e+35	81.64	7.51	0.71	2.59
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	519	MAX VALUE	190.06	0.00	0.00	0.00

Dual graph

Density: 10.09%
MCB compute time (ms): 37
MCB cycles: 446
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/Dual1.json

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

Clustering coefficient 0.33 1.00 0.52 0.50 53.80 0.00 -68.37 0.10 0.18 3.48

Degree 3 18 10.29 10.00 1,060 MAX VALUE 234.68 3.18 0.31 2.48

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.17 3.00 1,414 MAX VALUE 510.54 0.49 0.15 0.47

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.33	1.00	0.52	0.50	53.80	0.00	-68.37	0.10	0.18	3.48
Degree	3	18	10.29	10.00	1,060	MAX VALUE	234.68	3.18	0.31	2.48
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.17	3.00	1,414	MAX VALUE	510.54	0.49	0.15	0.47

Minimal dual graph

Density: 3.16%
MCB compute time (ms): 10
MCB cycles: 68

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

Clustering coefficient 0.00 0.00 None 0.00 None None None None None 0.57

Degree 1 5 3.22 3.00 332 MAX VALUE 117.70 0.72 0.22 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.85 7.00 466 MAX VALUE 129.57 1.26 0.18 1.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.00	None	0.00	None	None	None	None	None	0.57
Degree	1	5	3.22	3.00	332	MAX VALUE	117.70	0.72	0.22	1.08
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.85	7.00	466	MAX VALUE	129.57	1.26	0.18	1.52

Triangulated dual graph

Density: 34.53%
Triangles: 20,255

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

Clustering coefficient 0.61 1.00 0.80 0.79 82.85 0.00 -23.37 0.11 0.14 4.16

Degree 3 68 35.22 37.00 3,628 MAX VALUE 339.32 20.69 0.59 3.71

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	0.61	1.00	0.80	0.79	82.85	0.00	-23.37	0.11	0.14	4.16
Degree	3	68	35.22	37.00	3,628	MAX VALUE	339.32	20.69	0.59	3.71
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.07%

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

Clustering coefficient 0.33 1.00 None 0.67 None None None None None 3.13

Degree 1 37 12.31 5.00 1,268 MAX VALUE 206.83 12.01 0.98 2.86

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	0.33	1.00	None	0.67	None	None	None	None	None	3.13
Degree	1	37	12.31	5.00	1,268	MAX VALUE	206.83	12.01	0.98	2.86
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.03%
MCB compute time (ms): 13
MCB cycles: 64
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-56-ext/Incidence1.json

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

Clustering coefficient 0.00 0.00 None 0.00 None None None None None 0.56

Degree 1 11 2.88 2.00 412 MAX VALUE 132.67 1.85 0.64 1.06

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.44 8.00 476 MAX VALUE 127.52 1.25 0.17 0.93

XCSP 2.1 Benchmarks