XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-40-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 2 21 12.47 12.00 112,224 MAX VALUE 22,519.70 2.48 0.20 2.33

Relational linkage 0.08 0.56 0.36 0.36 357.32 0.00 -1,046.67 0.06 0.18 1.87

Tightness 0.44 0.56 0.50 0.50 90.22 0.00 -124.46 0.02 0.04 3.69

Tuples 272 350 311.73 312.00 56,112 MAX VALUE 1,033.45 12.06 0.04 3.69

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

Value table constraints 3 15 9.00 9.00 360 1.77e+37 85.77 2.78 0.31 2.28

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	2	21	12.47	12.00	112,224	MAX VALUE	22,519.70	2.48	0.20	2.33
Relational linkage	0.08	0.56	0.36	0.36	357.32	0.00	-1,046.67	0.06	0.18	1.87
Tightness	0.44	0.56	0.50	0.50	90.22	0.00	-124.46	0.02	0.04	3.69
Tuples	272	350	311.73	312.00	56,112	MAX VALUE	1,033.45	12.06	0.04	3.69
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	3	15	9.00	9.00	360	1.77e+37	85.77	2.78	0.31	2.28
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: 20
Number of leaves: 11
Tree depth: 4
CIR: 0.10
Independent Cluster Pairs: 17
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/Tree1.json

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

Cluster constraints 4 59 22.25 18.00 445 4.50e+24 56.77 16.44 0.74 2.65

Variables per cluster 4 20 10.65 9.50 213 5.54e+19 45.46 4.61 0.43 2.32

Separator constraints 0 49 13.25 9.50 265 0 None 13.99 1.06 2.62

Separator variables 0 18 8.65 8.00 173 0 None 4.43 0.51 2.39

Clusters per var 1 12 5.33 5.50 213 6.73e+22 52.56 3.68 0.69 2.19

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	59	22.25	18.00	445	4.50e+24	56.77	16.44	0.74	2.65
Variables per cluster	4	20	10.65	9.50	213	5.54e+19	45.46	4.61	0.43	2.32
Separator constraints	0	49	13.25	9.50	265	0	None	13.99	1.06	2.62
Separator variables	0	18	8.65	8.00	173	0	None	4.43	0.51	2.39
Clusters per var	1	12	5.33	5.50	213	6.73e+22	52.56	3.68	0.69	2.19

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.22
Independent Cluster Pairs: 147
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/DualTree1.json

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

Cluster constraints 26 362 127.45 93.00 4,843 MAX VALUE 175.13 91.73 0.72 3.44

Variables per cluster 10 85 28.89 22.00 1,098 MAX VALUE 121.07 19.13 0.66 3.09

Separator constraints 0 224 85.47 65.00 3,248 0 None 57.54 0.67 3.46

Separator variables 0 65 24.16 20.00 918 0 None 14.76 0.61 3.21

Clusters per variable 1 11 6.10 7.00 1,098 MAX VALUE 294.75 2.75 0.45 2.22

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	26	362	127.45	93.00	4,843	MAX VALUE	175.13	91.73	0.72	3.44
Variables per cluster	10	85	28.89	22.00	1,098	MAX VALUE	121.07	19.13	0.66	3.09
Separator constraints	0	224	85.47	65.00	3,248	0	None	57.54	0.67	3.46
Separator variables	0	65	24.16	20.00	918	0	None	14.76	0.61	3.21
Clusters per variable	1	11	6.10	7.00	1,098	MAX VALUE	294.75	2.75	0.45	2.22

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 155
Triangles: 132
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/Primal1.json

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

Clustering coefficient 0.14 0.40 0.26 0.25 10.26 0.00 -55.57 0.06 0.24 3.21

Degree 3 15 9.00 9.00 360 1.77e+37 85.77 2.78 0.31 2.28

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.26 3.00 506 MAX VALUE 182.08 0.44 0.14 0.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.14	0.40	0.26	0.25	10.26	0.00	-55.57	0.06	0.24	3.21
Degree	3	15	9.00	9.00	360	1.77e+37	85.77	2.78	0.31	2.28
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.26	3.00	506	MAX VALUE	182.08	0.44	0.14	0.58

Triangulated primal graph

Density: 48.97%
MCB compute time (ms): 8
MCB cycles: 359
Triangles: 2,169

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

Clustering coefficient 0.64 1.00 0.83 0.81 33.36 0.00 -7.70 0.12 0.15 2.96

Degree 3 31 19.10 24.00 764 MAX VALUE 110.59 9.52 0.50 2.88

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,077 MAX VALUE 394.40 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.64	1.00	0.83	0.81	33.36	0.00	-7.70	0.12	0.15	2.96
Degree	3	31	19.10	24.00	764	MAX VALUE	110.59	9.52	0.50	2.88
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,077	MAX VALUE	394.40	0.00	0.00	0.00

Dual graph

Density: 9.90%
MCB compute time (ms): 182
MCB cycles: 2,213
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/Dual1.json

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

Clustering coefficient 0.46 0.75 0.51 0.50 92.39 0.00 -120.60 0.04 0.08 4.35

Degree 9 27 17.72 17.00 3,190 MAX VALUE 513.43 3.68 0.21 2.67

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.33 3.00 7,364 MAX VALUE 2,635.15 0.53 0.16 0.71

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	0.75	0.51	0.50	92.39	0.00	-120.60	0.04	0.08	4.35
Degree	9	27	17.72	17.00	3,190	MAX VALUE	513.43	3.68	0.21	2.67
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.33	3.00	7,364	MAX VALUE	2,635.15	0.53	0.16	0.71

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 75
MCB cycles: 141

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 6 3.56 3.00 640 MAX VALUE 224.43 0.74 0.21 1.10

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.70 7.00 944 MAX VALUE 265.50 1.21 0.18 1.53

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	6	3.56	3.00	640	MAX VALUE	224.43	0.74	0.21	1.10
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.70	7.00	944	MAX VALUE	265.50	1.21	0.18	1.53

Triangulated dual graph

Density: 46.55%
Triangles: 199,882

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

Clustering coefficient 0.69 1.00 0.84 0.82 150.62 0.00 -33.03 0.09 0.10 4.61

Degree 9 135 83.33 98.50 15,000 MAX VALUE 758.64 41.26 0.50 4.00

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	0.69	1.00	0.84	0.82	150.62	0.00	-33.03	0.09	0.10	4.61
Degree	9	135	83.33	98.50	15,000	MAX VALUE	758.64	41.26	0.50	4.00
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 0.53 1.00 0.80 0.74 144.04 0.00 -43.56 0.16 0.20 3.34

Degree 2 66 21.06 7.00 3,790 MAX VALUE 421.55 23.09 1.10 3.03

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	0.80	0.74	144.04	0.00	-43.56	0.16	0.20	3.34
Degree	2	66	21.06	7.00	3,790	MAX VALUE	421.55	23.09	1.10	3.03
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 41
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-40-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 15 3.27 2.00 720 MAX VALUE 210.54 2.95 0.90 0.89

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.38 6.00 900 MAX VALUE 260.41 0.79 0.12 0.49

XCSP 2.1 Benchmarks