XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-80-103-800-84-ext
Number of variables: 40
Number of constraints: 103
Satisfiable: True
Timestamp: 2025-07-20 22:09:38
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 5 31 15.96 16.00 261,691 MAX VALUE 44,988.50 3.58 0.22 2.69

Relational linkage 0.06 0.26 0.15 0.15 468.29 0.00 -5,985.10 0.03 0.20 2.31

Tightness 0.79 0.81 0.80 0.80 82.45 0.00 -22.92 0.00 0.01 4.13

Tuples 1,214 1,363 1,276.58 1,282.00 131,488 MAX VALUE 736.62 31.40 0.02 4.13

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

Value table constraints 2 9 5.26 5.00 205 6.88e+26 61.80 1.92 0.36 1.97

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	5	31	15.96	16.00	261,691	MAX VALUE	44,988.50	3.58	0.22	2.69
Relational linkage	0.06	0.26	0.15	0.15	468.29	0.00	-5,985.10	0.03	0.20	2.31
Tightness	0.79	0.81	0.80	0.80	82.45	0.00	-22.92	0.00	0.01	4.13
Tuples	1,214	1,363	1,276.58	1,282.00	131,488	MAX VALUE	736.62	31.40	0.02	4.13
Values	80	80	80.00	80.00	3,200	MAX VALUE	175.28	0.00	0.00	0.00
Value table constraints	2	9	5.26	5.00	205	6.88e+26	61.80	1.92	0.36	1.97
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: 0.40
Independent Cluster Pairs: 139
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/Tree1.json

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

Cluster constraints 1 14 5.43 4.00 152 2.89e+18 42.51 3.17 0.58 2.12

Variables per cluster 2 13 6.11 5.00 171 5.39e+20 47.74 2.88 0.47 2.12

Separator constraints 0 11 1.75 1.00 49 0 None 2.46 1.40 1.49

Separator variables 0 11 4.68 4.00 131 0 None 2.71 0.58 2.12

Clusters per var 1 13 4.28 2.50 171 5.15e+17 40.78 3.84 0.90 2.02

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	14	5.43	4.00	152	2.89e+18	42.51	3.17	0.58	2.12
Variables per cluster	2	13	6.11	5.00	171	5.39e+20	47.74	2.88	0.47	2.12
Separator constraints	0	11	1.75	1.00	49	0	None	2.46	1.40	1.49
Separator variables	0	11	4.68	4.00	131	0	None	2.71	0.58	2.12
Clusters per var	1	13	4.28	2.50	171	5.15e+17	40.78	3.84	0.90	2.02

Dual tree decomposition

Number of clusters: 38
Number of leaves: 12
Tree depth: 6
CIR: 0.43
Independent Cluster Pairs: 284
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/DualTree1.json

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

Cluster constraints 4 75 31.55 27.00 1,199 MAX VALUE 122.83 19.16 0.61 3.19

Variables per cluster 4 37 13.84 11.50 526 MAX VALUE 93.90 8.17 0.59 2.67

Separator constraints 0 47 18.18 15.50 691 0 None 11.89 0.65 3.25

Separator variables 0 29 11.13 10.00 423 0 None 6.41 0.58 2.71

Clusters per variable 1 11 5.11 5.00 526 MAX VALUE 145.40 2.87 0.56 2.18

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	75	31.55	27.00	1,199	MAX VALUE	122.83	19.16	0.61	3.19
Variables per cluster	4	37	13.84	11.50	526	MAX VALUE	93.90	8.17	0.59	2.67
Separator constraints	0	47	18.18	15.50	691	0	None	11.89	0.65	3.25
Separator variables	0	29	11.13	10.00	423	0	None	6.41	0.58	2.71
Clusters per variable	1	11	5.11	5.00	526	MAX VALUE	145.40	2.87	0.56	2.18

Primal graph

Density: 13.21%
MCB compute time (ms): 3
MCB cycles: 64
Triangles: 17
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/Primal1.json

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

Clustering coefficient None None None 0.10 None None None None None 2.22

Degree 1 9 5.15 5.00 206 6.88e+26 61.80 2.01 0.39 2.03

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.81 4.00 244 8.33e+36 85.01 0.53 0.14 0.78

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	None	None	None	0.10	None	None	None	None	None	2.22
Degree	1	9	5.15	5.00	206	6.88e+26	61.80	2.01	0.39	2.03
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.81	4.00	244	8.33e+36	85.01	0.53	0.14	0.78

Triangulated primal graph

Density: 26.79%
MCB compute time (ms): 4
MCB cycles: 173
Triangles: 630

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

Clustering coefficient None None None 0.75 None None None None None 2.77

Degree 1 24 10.45 8.00 418 1.30e+35 80.86 7.57 0.72 2.68

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	None	None	None	0.75	None	None	None	None	None	2.77
Degree	1	24	10.45	8.00	418	1.30e+35	80.86	7.57	0.72	2.68
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: 9.67%
MCB compute time (ms): 42
MCB cycles: 512
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/Dual1.json

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

Clustering coefficient 0.33 1.00 0.51 0.49 52.58 0.00 -70.30 0.08 0.16 3.18

Degree 3 15 9.86 10.00 1,016 MAX VALUE 231.98 2.41 0.24 2.24

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.50 3.00 1,790 MAX VALUE 628.98 0.81 0.23 0.84

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.33	1.00	0.51	0.49	52.58	0.00	-70.30	0.08	0.16	3.18
Degree	3	15	9.86	10.00	1,016	MAX VALUE	231.98	2.41	0.24	2.24
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.50	3.00	1,790	MAX VALUE	628.98	0.81	0.23	0.84

Minimal dual graph

Density: 3.16%
MCB compute time (ms): 15
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 4 3.22 3.00 332 MAX VALUE 118.48 0.62 0.19 0.93

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.89 7.00 441 MAX VALUE 122.15 1.32 0.19 1.54

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	4	3.22	3.00	332	MAX VALUE	118.48	0.62	0.19	0.93
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.89	7.00	441	MAX VALUE	122.15	1.32	0.19	1.54

Triangulated dual graph

Density: 32.80%
Triangles: 18,155

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

Clustering coefficient 0.60 1.00 0.80 0.76 82.28 0.00 -24.20 0.12 0.14 4.10

Degree 3 64 33.46 30.00 3,446 MAX VALUE 334.11 20.11 0.60 3.63

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	0.60	1.00	0.80	0.76	82.28	0.00	-24.20	0.12	0.14	4.10
Degree	3	64	33.46	30.00	3,446	MAX VALUE	334.11	20.11	0.60	3.63
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.09%

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

Clustering coefficient 0.42 1.00 0.76 0.67 78.60 0.00 -31.04 0.19 0.25 2.93

Degree 2 37 12.33 5.00 1,270 MAX VALUE 207.26 12.06 0.98 2.82

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	0.42	1.00	0.76	0.67	78.60	0.00	-31.04	0.19	0.25	2.93
Degree	2	37	12.33	5.00	1,270	MAX VALUE	207.26	12.06	0.98	2.82
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.03%
MCB compute time (ms): 17
MCB cycles: 64
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-84-ext/Incidence1.json

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

Clustering coefficient None None None 0.00 None None None None None 0.04

Degree 1 9 2.88 2.00 412 MAX VALUE 133.19 1.77 0.61 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.62 8.00 488 MAX VALUE 129.37 1.05 0.14 0.78

XCSP 2.1 Benchmarks