XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-180-84-900-81-ext
Number of variables: 40
Number of constraints: 84
Satisfiable: True
Timestamp: 2025-07-20 22:09:41
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 84

General features

Coarse blocks: 29,700
Value tables: 37

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

Arity 2 2 2.00 2.00 168 1.93e+25 58.22 0.00 0.00 0.00

Coarse blocks size 5 36 18.01 18.00 534,882 MAX VALUE 85,071.30 4.05 0.22 2.81

Relational linkage 0.03 0.14 0.08 0.08 515.36 0.00 -17,187.30 0.02 0.20 2.45

Tightness 0.90 0.90 0.90 0.90 75.60 0.00 -8.85 0.00 0.00 4.11

Tuples 3,146 3,394 3,241.36 3,242.00 272,274 MAX VALUE 679.03 45.58 0.01 4.11

Values 180 180 180.00 180.00 7,200 MAX VALUE 207.72 0.00 0.00 0.00

Value table constraints 2 9 4.46 5.00 165 4.25e+22 52.10 1.73 0.39 1.76

Value table partitions 180 180 180.00 180.00 6,660 MAX VALUE 192.14 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	168	1.93e+25	58.22	0.00	0.00	0.00
Coarse blocks size	5	36	18.01	18.00	534,882	MAX VALUE	85,071.30	4.05	0.22	2.81
Relational linkage	0.03	0.14	0.08	0.08	515.36	0.00	-17,187.30	0.02	0.20	2.45
Tightness	0.90	0.90	0.90	0.90	75.60	0.00	-8.85	0.00	0.00	4.11
Tuples	3,146	3,394	3,241.36	3,242.00	272,274	MAX VALUE	679.03	45.58	0.01	4.11
Values	180	180	180.00	180.00	7,200	MAX VALUE	207.72	0.00	0.00	0.00
Value table constraints	2	9	4.46	5.00	165	4.25e+22	52.10	1.73	0.39	1.76
Value table partitions	180	180	180.00	180.00	6,660	MAX VALUE	192.14	0.00	0.00	0.00

Tree decomposition

Number of clusters: 31
Number of leaves: 14
Tree depth: 6
CIR: 0.47
Independent Cluster Pairs: 203
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/Tree1.json

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

Cluster constraints 1 10 4.65 4.00 144 1.03e+18 41.47 2.63 0.57 2.10

Variables per cluster 2 10 5.39 5.00 167 9.37e+20 48.29 2.68 0.50 1.91

Separator constraints 0 8 1.94 1.00 60 0 None 2.46 1.27 1.70

Separator variables 0 9 4.10 4.00 127 0 None 2.66 0.65 1.99

Clusters per var 1 14 4.17 2.00 167 6.10e+16 38.65 3.98 0.95 2.03

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	10	4.65	4.00	144	1.03e+18	41.47	2.63	0.57	2.10
Variables per cluster	2	10	5.39	5.00	167	9.37e+20	48.29	2.68	0.50	1.91
Separator constraints	0	8	1.94	1.00	60	0	None	2.46	1.27	1.70
Separator variables	0	9	4.10	4.00	127	0	None	2.66	0.65	1.99
Clusters per var	1	14	4.17	2.00	167	6.10e+16	38.65	3.98	0.95	2.03

Dual tree decomposition

Number of clusters: 38
Number of leaves: 14
Tree depth: 6
CIR: 0.51
Independent Cluster Pairs: 339
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/DualTree1.json

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

Cluster constraints 4 51 18.97 16.50 721 MAX VALUE 105.71 10.68 0.56 3.04

Variables per cluster 4 25 10.37 8.00 394 4.39e+36 84.37 5.29 0.51 2.62

Separator constraints 0 29 10.00 10.00 380 0 None 6.47 0.65 2.69

Separator variables 0 18 8.16 7.00 310 0 None 4.07 0.50 2.53

Clusters per variable 1 10 4.69 4.00 394 MAX VALUE 110.28 2.75 0.59 2.22

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	51	18.97	16.50	721	MAX VALUE	105.71	10.68	0.56	3.04
Variables per cluster	4	25	10.37	8.00	394	4.39e+36	84.37	5.29	0.51	2.62
Separator constraints	0	29	10.00	10.00	380	0	None	6.47	0.65	2.69
Separator variables	0	18	8.16	7.00	310	0	None	4.07	0.50	2.53
Clusters per variable	1	10	4.69	4.00	394	MAX VALUE	110.28	2.75	0.59	2.22

Primal graph

Density: 10.77%
MCB compute time (ms): 1
MCB cycles: 45
Triangles: 15
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 None 0.11 None None None None None 2.36

Degree 1 9 4.20 4.00 168 4.25e+22 52.10 1.90 0.45 1.89

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.96 4.00 178 3.21e+26 61.03 0.76 0.19 1.08

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	None	0.11	None	None	None	None	None	2.36
Degree	1	9	4.20	4.00	168	4.25e+22	52.10	1.90	0.45	1.89
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.96	4.00	178	3.21e+26	61.03	0.76	0.19	1.08

Triangulated primal graph

Density: 22.05%
MCB compute time (ms): 2
MCB cycles: 139
Triangles: 426

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

Clustering coefficient 0.45 1.00 None 0.79 None None None None None 3.19

Degree 1 22 8.60 5.00 344 3.63e+30 70.37 6.75 0.79 2.61

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 417 MAX VALUE 152.71 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	1.00	None	0.79	None	None	None	None	None	3.19
Degree	1	22	8.60	5.00	344	3.63e+30	70.37	6.75	0.79	2.61
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	417	MAX VALUE	152.71	0.00	0.00	0.00

Dual graph

Density: 9.78%
MCB compute time (ms): 15
MCB cycles: 270
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/Dual1.json

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

Clustering coefficient 0.33 1.00 0.53 0.49 44.33 0.00 -55.66 0.13 0.24 2.98

Degree 3 14 8.12 8.00 682 MAX VALUE 172.25 2.26 0.28 2.16

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.22 3.00 870 MAX VALUE 312.68 0.56 0.17 0.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.33	1.00	0.53	0.49	44.33	0.00	-55.66	0.13	0.24	2.98
Degree	3	14	8.12	8.00	682	MAX VALUE	172.25	2.26	0.28	2.16
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.22	3.00	870	MAX VALUE	312.68	0.56	0.17	0.55

Minimal dual graph

Density: 3.67%
MCB compute time (ms): 6
MCB cycles: 45

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 0.90

Degree 1 4 3.05 3.00 256 MAX VALUE 90.86 0.71 0.23 1.04

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.96 8.00 313 2.09e+37 85.94 1.62 0.23 1.71

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	0.90
Degree	1	4	3.05	3.00	256	MAX VALUE	90.86	0.71	0.23	1.04
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.96	8.00	313	2.09e+37	85.94	1.62	0.23	1.71

Triangulated dual graph

Density: 27.37%
Triangles: 6,382

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

Clustering coefficient 0.55 1.00 0.78 0.78 65.25 0.00 -22.52 0.14 0.18 3.77

Degree 3 47 22.71 20.50 1,908 MAX VALUE 240.63 14.08 0.62 3.44

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	0.55	1.00	0.78	0.78	65.25	0.00	-22.52	0.14	0.18	3.77
Degree	3	47	22.71	20.50	1,908	MAX VALUE	240.63	14.08	0.62	3.44
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.76%

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 3.10

Degree 1 29 9.76 5.00 820 MAX VALUE 153.82 9.15 0.94 2.69

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	3.10
Degree	1	29	9.76	5.00	820	MAX VALUE	153.82	9.15	0.94	2.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.20%
MCB compute time (ms): 8
MCB cycles: 45
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-81-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 0.88

Degree 1 9 2.71 2.00 336 MAX VALUE 110.33 1.49 0.55 1.02

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.91 8.00 356 MAX VALUE 92.22 1.52 0.19 1.08

XCSP 2.1 Benchmarks