XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-67-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:28
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 180

General features

Coarse blocks: 9,000
Value tables: 40

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

Arity 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00

Coarse blocks size 3 22 12.45 12.00 112,022 MAX VALUE 22,500.70 2.49 0.20 2.33

Relational linkage 0.12 0.60 0.35 0.36 352.80 0.00 -1,057.39 0.06 0.17 1.82

Tightness 0.47 0.55 0.50 0.50 90.38 0.00 -124.12 0.02 0.04 3.67

Tuples 279 333 311.17 312.00 56,011 MAX VALUE 1,033.14 11.22 0.04 3.67

Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Value table constraints 4 14 9.00 8.50 360 3.82e+37 86.54 2.30 0.26 2.12

Value table partitions 25 25 25.00 25.00 1,000 MAX VALUE 128.75 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	360	MAX VALUE	124.77	0.00	0.00	0.00
Coarse blocks size	3	22	12.45	12.00	112,022	MAX VALUE	22,500.70	2.49	0.20	2.33
Relational linkage	0.12	0.60	0.35	0.36	352.80	0.00	-1,057.39	0.06	0.17	1.82
Tightness	0.47	0.55	0.50	0.50	90.38	0.00	-124.12	0.02	0.04	3.67
Tuples	279	333	311.17	312.00	56,011	MAX VALUE	1,033.14	11.22	0.04	3.67
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	14	9.00	8.50	360	3.82e+37	86.54	2.30	0.26	2.12
Value table partitions	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00

Tree decomposition

Number of clusters: 19
Number of leaves: 10
Tree depth: 4
CIR: 0.05
Independent Cluster Pairs: 8
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/Tree1.json

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

Cluster constraints 4 59 21.74 15.00 413 2.88e+23 54.02 15.42 0.71 2.60

Variables per cluster 5 22 11.79 10.00 224 4.07e+19 45.15 5.16 0.44 2.36

Separator constraints 0 49 12.26 7.00 233 0 None 13.14 1.07 2.45

Separator variables 0 21 9.68 8.00 184 0 None 5.10 0.53 2.43

Clusters per var 1 12 5.60 7.00 224 1.19e+24 55.44 3.60 0.64 2.09

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	59	21.74	15.00	413	2.88e+23	54.02	15.42	0.71	2.60
Variables per cluster	5	22	11.79	10.00	224	4.07e+19	45.15	5.16	0.44	2.36
Separator constraints	0	49	12.26	7.00	233	0	None	13.14	1.07	2.45
Separator variables	0	21	9.68	8.00	184	0	None	5.10	0.53	2.43
Clusters per var	1	12	5.60	7.00	224	1.19e+24	55.44	3.60	0.64	2.09

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.16
Independent Cluster Pairs: 104
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/DualTree1.json

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

Cluster constraints 36 360 126.71 98.50 4,815 MAX VALUE 175.97 86.05 0.68 3.53

Variables per cluster 12 84 29.82 23.00 1,133 MAX VALUE 122.45 19.55 0.66 3.14

Separator constraints 0 202 86.03 80.00 3,269 0 None 51.33 0.60 3.48

Separator variables 0 65 25.08 21.00 953 0 None 15.03 0.60 3.16

Clusters per variable 1 10 6.29 7.00 1,133 MAX VALUE 302.06 2.71 0.43 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	36	360	126.71	98.50	4,815	MAX VALUE	175.97	86.05	0.68	3.53
Variables per cluster	12	84	29.82	23.00	1,133	MAX VALUE	122.45	19.55	0.66	3.14
Separator constraints	0	202	86.03	80.00	3,269	0	None	51.33	0.60	3.48
Separator variables	0	65	25.08	21.00	953	0	None	15.03	0.60	3.16
Clusters per variable	1	10	6.29	7.00	1,133	MAX VALUE	302.06	2.71	0.43	2.15

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 151
Triangles: 106
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/Primal1.json

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

Clustering coefficient 0.00 0.38 0.19 0.21 7.72 0.00 None 0.07 0.38 3.11

Degree 4 14 9.00 8.50 360 3.82e+37 86.54 2.30 0.26 2.12

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.36 3.00 508 MAX VALUE 181.71 0.48 0.14 0.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.38	0.19	0.21	7.72	0.00	None	0.07	0.38	3.11
Degree	4	14	9.00	8.50	360	3.82e+37	86.54	2.30	0.26	2.12
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.36	3.00	508	MAX VALUE	181.71	0.48	0.14	0.66

Triangulated primal graph

Density: 53.21%
MCB compute time (ms): 6
MCB cycles: 441
Triangles: 2,586

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

Clustering coefficient 0.67 1.00 0.84 0.81 33.74 0.00 -7.13 0.11 0.13 3.04

Degree 4 32 20.75 27.00 830 MAX VALUE 114.80 9.62 0.46 2.59

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,323 MAX VALUE 484.49 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.67	1.00	0.84	0.81	33.74	0.00	-7.13	0.11	0.13	3.04
Degree	4	32	20.75	27.00	830	MAX VALUE	114.80	9.62	0.46	2.59
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,323	MAX VALUE	484.49	0.00	0.00	0.00

Dual graph

Density: 9.60%
MCB compute time (ms): 328
MCB cycles: 1,583
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/Dual1.json

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

Clustering coefficient 0.45 0.64 0.50 0.49 89.94 0.00 -125.19 0.03 0.06 4.08

Degree 11 26 17.18 17.00 3,092 MAX VALUE 508.52 3.29 0.19 2.55

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.16 3.00 5,005 MAX VALUE 1,812.04 0.39 0.12 0.46

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.64	0.50	0.49	89.94	0.00	-125.19	0.03	0.06	4.08
Degree	11	26	17.18	17.00	3,092	MAX VALUE	508.52	3.29	0.19	2.55
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.16	3.00	5,005	MAX VALUE	1,812.04	0.39	0.12	0.46

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 76
MCB cycles: 141

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

Clustering coefficient 0.00 0.33 0.00 0.00 0.83 0.00 None 0.04 7.99 0.10

Degree 2 5 3.56 3.00 640 MAX VALUE 224.95 0.69 0.19 1.02

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.72 7.00 947 MAX VALUE 266.06 1.18 0.18 1.53

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.83	0.00	None	0.04	7.99	0.10
Degree	2	5	3.56	3.00	640	MAX VALUE	224.95	0.69	0.19	1.02
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.72	7.00	947	MAX VALUE	266.06	1.18	0.18	1.53

Triangulated dual graph

Density: 48.54%
Triangles: 213,255

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

Clustering coefficient 0.70 1.00 0.84 0.82 150.69 0.00 -32.96 0.09 0.10 4.62

Degree 11 139 86.88 103.50 15,638 MAX VALUE 769.92 40.77 0.47 3.92

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	0.70	1.00	0.84	0.82	150.69	0.00	-32.96	0.09	0.10	4.62
Degree	11	139	86.88	103.50	15,638	MAX VALUE	769.92	40.77	0.47	3.92
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.41%

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

Clustering coefficient 0.52 1.00 0.79 0.75 141.96 0.00 -46.26 0.16 0.20 3.32

Degree 2 67 20.42 7.00 3,676 MAX VALUE 423.13 22.12 1.08 3.19

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	0.52	1.00	0.79	0.75	141.96	0.00	-46.26	0.16	0.20	3.32
Degree	2	67	20.42	7.00	3,676	MAX VALUE	423.13	22.12	1.08	3.19
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 40
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-67-ext/Incidence1.json

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 14 3.27 2.00 720 MAX VALUE 211.30 2.87 0.88 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.65 6.00 938 MAX VALUE 265.87 0.94 0.14 0.63

XCSP 2.1 Benchmarks