XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-180-84-900-74-ext
Number of variables: 40
Number of constraints: 84
Satisfiable: True
Timestamp: 2025-07-20 22:09:40
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 4 36 18.02 18.00 535,305 MAX VALUE 85,094.20 4.05 0.22 2.81

Relational linkage 0.02 0.14 0.08 0.08 515.11 0.00 -17,188.90 0.02 0.20 2.45

Tightness 0.90 0.90 0.90 0.90 75.59 0.00 -8.86 0.00 0.00 4.23

Tuples 3,119 3,366 3,244.27 3,246.00 272,519 MAX VALUE 679.10 57.89 0.02 4.23

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

Value table constraints 2 8 4.46 4.00 165 6.41e+22 52.52 1.69 0.38 1.68

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	4	36	18.02	18.00	535,305	MAX VALUE	85,094.20	4.05	0.22	2.81
Relational linkage	0.02	0.14	0.08	0.08	515.11	0.00	-17,188.90	0.02	0.20	2.45
Tightness	0.90	0.90	0.90	0.90	75.59	0.00	-8.86	0.00	0.00	4.23
Tuples	3,119	3,366	3,244.27	3,246.00	272,519	MAX VALUE	679.10	57.89	0.02	4.23
Values	180	180	180.00	180.00	7,200	MAX VALUE	207.72	0.00	0.00	0.00
Value table constraints	2	8	4.46	4.00	165	6.41e+22	52.52	1.69	0.38	1.68
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: 12
Tree depth: 6
CIR: 0.57
Independent Cluster Pairs: 246
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/Tree1.json

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

Cluster constraints 1 10 4.39 5.00 136 2.72e+17 40.15 2.35 0.54 2.07

Variables per cluster 2 10 5.32 5.00 165 9.56e+20 48.31 2.44 0.46 2.12

Separator constraints 0 6 1.68 1.00 52 0 None 1.87 1.12 1.58

Separator variables 0 9 4.03 4.00 125 0 None 2.40 0.60 2.17

Clusters per var 1 12 4.12 2.50 165 7.93e+17 41.21 3.44 0.83 2.05

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	10	4.39	5.00	136	2.72e+17	40.15	2.35	0.54	2.07
Variables per cluster	2	10	5.32	5.00	165	9.56e+20	48.31	2.44	0.46	2.12
Separator constraints	0	6	1.68	1.00	52	0	None	1.87	1.12	1.58
Separator variables	0	9	4.03	4.00	125	0	None	2.40	0.60	2.17
Clusters per var	1	12	4.12	2.50	165	7.93e+17	41.21	3.44	0.83	2.05

Dual tree decomposition

Number of clusters: 38
Number of leaves: 13
Tree depth: 7
CIR: 0.53
Independent Cluster Pairs: 353
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/DualTree1.json

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

Cluster constraints 1 37 18.11 18.00 688 MAX VALUE 102.98 9.43 0.52 3.06

Variables per cluster 2 23 10.11 9.00 384 1.44e+36 83.26 4.98 0.49 2.60

Separator constraints 0 21 9.21 8.00 350 0 None 5.45 0.59 2.59

Separator variables 0 16 7.89 7.50 300 0 None 3.87 0.49 2.50

Clusters per variable 1 11 4.57 4.00 384 MAX VALUE 108.87 2.70 0.59 2.25

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	37	18.11	18.00	688	MAX VALUE	102.98	9.43	0.52	3.06
Variables per cluster	2	23	10.11	9.00	384	1.44e+36	83.26	4.98	0.49	2.60
Separator constraints	0	21	9.21	8.00	350	0	None	5.45	0.59	2.59
Separator variables	0	16	7.89	7.50	300	0	None	3.87	0.49	2.50
Clusters per variable	1	11	4.57	4.00	384	MAX VALUE	108.87	2.70	0.59	2.25

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-2-40-180-84-900-74-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/Primal1.json

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

Clustering coefficient None None None 0.13 None None None None None 2.29

Degree 1 8 4.20 4.00 168 6.41e+22 52.52 1.86 0.44 1.82

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.96 4.00 178 3.01e+26 60.97 0.79 0.20 1.09

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	None	None	None	0.13	None	None	None	None	None	2.29
Degree	1	8	4.20	4.00	168	6.41e+22	52.52	1.86	0.44	1.82
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.96	4.00	178	3.01e+26	60.97	0.79	0.20	1.09

Triangulated primal graph

Density: 21.79%
MCB compute time (ms): 2
MCB cycles: 166
Triangles: 399

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

Clustering coefficient None None None 0.69 None None None None None 3.13

Degree 1 20 8.50 6.50 340 1.31e+31 71.65 6.17 0.73 2.75

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.01 3.00 499 MAX VALUE 182.66 0.08 0.03 0.04

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	None	None	None	0.69	None	None	None	None	None	3.13
Degree	1	20	8.50	6.50	340	1.31e+31	71.65	6.17	0.73	2.75
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.01	3.00	499	MAX VALUE	182.66	0.08	0.03	0.04

Dual graph

Density: 9.70%
MCB compute time (ms): 17
MCB cycles: 265
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/Dual1.json

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

Clustering coefficient 0.40 1.00 None 0.50 None None None None None 2.73

Degree 1 13 8.05 8.00 676 MAX VALUE 170.33 2.40 0.30 2.19

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.24 3.00 858 MAX VALUE 307.73 0.60 0.19 0.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	1.00	None	0.50	None	None	None	None	None	2.73
Degree	1	13	8.05	8.00	676	MAX VALUE	170.33	2.40	0.30	2.19
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.24	3.00	858	MAX VALUE	307.73	0.60	0.19	0.54

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 0.33 None 0.00 None None None None None 0.22

Degree 1 4 3.05 3.00 256 MAX VALUE 91.50 0.63 0.21 0.95

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 7.04 7.00 317 3.28e+37 86.39 1.62 0.23 1.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	None	0.00	None	None	None	None	None	0.22
Degree	1	4	3.05	3.00	256	MAX VALUE	91.50	0.63	0.21	0.95
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	7.04	7.00	317	3.28e+37	86.39	1.62	0.23	1.69

Triangulated dual graph

Density: 25.82%
Triangles: 5,574

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

Clustering coefficient 0.53 1.00 None 0.74 None None None None None 4.03

Degree 1 44 21.43 20.00 1,800 MAX VALUE 235.89 13.17 0.61 3.48

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	0.53	1.00	None	0.74	None	None	None	None	None	4.03
Degree	1	44	21.43	20.00	1,800	MAX VALUE	235.89	13.17	0.61	3.48
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.82%

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 3.06

Degree 1 31 9.81 5.00 824 MAX VALUE 156.30 9.05 0.92 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	3.06
Degree	1	31	9.81	5.00	824	MAX VALUE	156.30	9.05	0.92	2.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.20%
MCB compute time (ms): 9
MCB cycles: 45
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-74-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 0.92

Degree 1 8 2.71 2.00 336 MAX VALUE 110.74 1.47 0.54 1.06

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.91 8.00 356 MAX VALUE 92.16 1.58 0.20 1.09

XCSP 2.1 Benchmarks