XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-80-103-800-35-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 15.98 16.00 262,143 MAX VALUE 45,019.20 3.59 0.22 2.69

Relational linkage 0.05 0.28 0.15 0.15 471.74 0.00 -5,962.99 0.03 0.21 2.32

Tightness 0.79 0.82 0.80 0.80 82.42 0.00 -22.96 0.00 0.01 4.10

Tuples 1,180 1,360 1,278.97 1,281.00 131,734 MAX VALUE 736.81 31.56 0.02 4.10

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 5.00 205 1.85e+26 60.48 2.37 0.45 2.10

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	15.98	16.00	262,143	MAX VALUE	45,019.20	3.59	0.22	2.69
Relational linkage	0.05	0.28	0.15	0.15	471.74	0.00	-5,962.99	0.03	0.21	2.32
Tightness	0.79	0.82	0.80	0.80	82.42	0.00	-22.96	0.00	0.01	4.10
Tuples	1,180	1,360	1,278.97	1,281.00	131,734	MAX VALUE	736.81	31.56	0.02	4.10
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	5.00	205	1.85e+26	60.48	2.37	0.45	2.10
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: 15
Tree depth: 4
CIR: 0.41
Independent Cluster Pairs: 145
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/Tree1.json

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

Cluster constraints 1 17 6.11 4.00 171 1.37e+19 44.06 4.14 0.68 2.41

Variables per cluster 2 13 5.93 5.00 166 1.94e+20 46.71 2.91 0.49 2.03

Separator constraints 0 12 2.43 1.00 68 0 None 3.04 1.25 1.82

Separator variables 0 12 4.50 4.00 126 0 None 2.72 0.60 2.08

Clusters per var 1 12 4.15 2.00 166 1.85e+17 39.76 3.64 0.88 1.97

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	17	6.11	4.00	171	1.37e+19	44.06	4.14	0.68	2.41
Variables per cluster	2	13	5.93	5.00	166	1.94e+20	46.71	2.91	0.49	2.03
Separator constraints	0	12	2.43	1.00	68	0	None	3.04	1.25	1.82
Separator variables	0	12	4.50	4.00	126	0	None	2.72	0.60	2.08
Clusters per var	1	12	4.15	2.00	166	1.85e+17	39.76	3.64	0.88	1.97

Dual tree decomposition

Number of clusters: 38
Number of leaves: 13
Tree depth: 7
CIR: 0.40
Independent Cluster Pairs: 268
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/DualTree1.json

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

Cluster constraints 4 107 34.11 26.50 1,296 MAX VALUE 122.16 25.57 0.75 3.33

Variables per cluster 4 39 13.89 11.00 528 MAX VALUE 93.93 8.51 0.61 2.79

Separator constraints 0 60 19.74 17.50 750 0 None 15.72 0.80 3.15

Separator variables 0 30 11.18 9.50 425 0 None 6.60 0.59 2.91

Clusters per variable 1 12 5.13 5.00 528 MAX VALUE 145.36 2.95 0.57 2.34

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	107	34.11	26.50	1,296	MAX VALUE	122.16	25.57	0.75	3.33
Variables per cluster	4	39	13.89	11.00	528	MAX VALUE	93.93	8.51	0.61	2.79
Separator constraints	0	60	19.74	17.50	750	0	None	15.72	0.80	3.15
Separator variables	0	30	11.18	9.50	425	0	None	6.60	0.59	2.91
Clusters per variable	1	12	5.13	5.00	528	MAX VALUE	145.36	2.95	0.57	2.34

Primal graph

Density: 13.21%
MCB compute time (ms): 2
MCB cycles: 65
Triangles: 35
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 None 0.18 None None None None None 2.57

Degree 1 11 5.15 5.00 206 1.85e+26 60.48 2.43 0.47 2.16

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.65 3.00 237 8.95e+35 82.78 0.75 0.21 1.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	None	0.18	None	None	None	None	None	2.57
Degree	1	11	5.15	5.00	206	1.85e+26	60.48	2.43	0.47	2.16
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.65	3.00	237	8.95e+35	82.78	0.75	0.21	1.00

Triangulated primal graph

Density: 26.15%
MCB compute time (ms): 3
MCB cycles: 170
Triangles: 610

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

Clustering coefficient 0.48 1.00 None 0.74 None None None None None 2.84

Degree 1 23 10.20 7.00 408 2.09e+34 79.03 7.52 0.74 2.60

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 510 MAX VALUE 186.76 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	1.00	None	0.74	None	None	None	None	None	2.84
Degree	1	23	10.20	7.00	408	2.09e+34	79.03	7.52	0.74	2.60
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	510	MAX VALUE	186.76	0.00	0.00	0.00

Dual graph

Density: 10.39%
MCB compute time (ms): 45
MCB cycles: 452
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/Dual1.json

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

Clustering coefficient 0.33 1.00 0.53 0.50 54.78 0.00 -66.62 0.10 0.19 3.64

Degree 3 18 10.60 11.00 1,092 MAX VALUE 237.40 3.33 0.31 2.55

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.11 3.00 1,406 MAX VALUE 509.91 0.42 0.13 0.34

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.33	1.00	0.53	0.50	54.78	0.00	-66.62	0.10	0.19	3.64
Degree	3	18	10.60	11.00	1,092	MAX VALUE	237.40	3.33	0.31	2.55
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.11	3.00	1,406	MAX VALUE	509.91	0.42	0.13	0.34

Minimal dual graph

Density: 3.16%
MCB compute time (ms): 11
MCB cycles: 64

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 5 3.22 3.00 332 MAX VALUE 117.93 0.71 0.22 1.07

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.69 7.00 428 MAX VALUE 120.33 1.31 0.20 1.63

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	5	3.22	3.00	332	MAX VALUE	117.93	0.71	0.22	1.07
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.69	7.00	428	MAX VALUE	120.33	1.31	0.20	1.63

Triangulated dual graph

Density: 34.04%
Triangles: 19,810

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

Clustering coefficient 0.61 1.00 0.81 0.79 83.02 0.00 -23.19 0.11 0.14 4.05

Degree 3 65 34.72 35.00 3,576 MAX VALUE 337.59 20.79 0.60 3.52

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	0.81	0.79	83.02	0.00	-23.19	0.11	0.14	4.05
Degree	3	65	34.72	35.00	3,576	MAX VALUE	337.59	20.79	0.60	3.52
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.01%

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

Clustering coefficient 0.46 1.00 0.76 0.67 77.87 0.00 -31.93 0.19 0.25 2.97

Degree 2 40 12.25 5.00 1,262 MAX VALUE 206.71 12.02 0.98 2.84

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	0.46	1.00	0.76	0.67	77.87	0.00	-31.93	0.19	0.25	2.97
Degree	2	40	12.25	5.00	1,262	MAX VALUE	206.71	12.02	0.98	2.84
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-2-40-80-103-800-35-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-35-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 0.47

Degree 1 11 2.88 2.00 412 MAX VALUE 131.87 1.91 0.66 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.28 6.00 466 MAX VALUE 125.76 1.52 0.21 1.00

XCSP 2.1 Benchmarks