XCSP 2.1 Benchmark Database

Instance: normalized-hole-08-ext
Number of variables: 72
Number of constraints: 297
Satisfiable: True
Timestamp: 2025-07-20 22:09:44
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 72
Number of constraints: 297

General features

Coarse blocks: 1,296
Value tables: 72

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

Arity 2 8 2.18 2.00 648 MAX VALUE 218.34 1.03 0.47 0.14

Coarse blocks size 1 128 15.50 2.00 20,088 MAX VALUE 1,097.38 39.60 2.55 1.04

Relational linkage 0.50 0.99 0.75 0.75 107.44 0.00 -50.47 0.25 0.33 0.69

Tightness 0.00 0.25 0.24 0.25 72.04 0.00 -449.16 0.04 0.17 0.14

Tuples 3 255 10.64 3.00 3,159 MAX VALUE 366.27 43.20 4.06 0.14

Values 2 2 2.00 2.00 144 4.72e+21 49.91 0.00 0.00 0.00

Value table constraints 9 9 9.00 9.00 648 MAX VALUE 158.20 0.00 0.00 0.00

Value table partitions 2 2 2.00 2.00 144 4.72e+21 49.91 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	8	2.18	2.00	648	MAX VALUE	218.34	1.03	0.47	0.14
Coarse blocks size	1	128	15.50	2.00	20,088	MAX VALUE	1,097.38	39.60	2.55	1.04
Relational linkage	0.50	0.99	0.75	0.75	107.44	0.00	-50.47	0.25	0.33	0.69
Tightness	0.00	0.25	0.24	0.25	72.04	0.00	-449.16	0.04	0.17	0.14
Tuples	3	255	10.64	3.00	3,159	MAX VALUE	366.27	43.20	4.06	0.14
Values	2	2	2.00	2.00	144	4.72e+21	49.91	0.00	0.00	0.00
Value table constraints	9	9	9.00	9.00	648	MAX VALUE	158.20	0.00	0.00	0.00
Value table partitions	2	2	2.00	2.00	144	4.72e+21	49.91	0.00	0.00	0.00

Tree decomposition

Number of clusters: 15
Number of leaves: 8
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/Tree1.json

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

Cluster constraints 36 112 53.67 37.00 805 2.44e+25 58.46 24.87 0.46 1.38

Variables per cluster 16 46 23.80 16.00 357 1.39e+20 46.38 10.09 0.42 1.38

Separator constraints 0 64 33.87 28.00 508 0 None 14.52 0.43 1.02

Separator variables 0 36 19.00 15.00 285 0 None 8.37 0.44 1.38

Clusters per var 1 7 4.96 6.00 357 MAX VALUE 106.59 1.79 0.36 1.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	36	112	53.67	37.00	805	2.44e+25	58.46	24.87	0.46	1.38
Variables per cluster	16	46	23.80	16.00	357	1.39e+20	46.38	10.09	0.42	1.38
Separator constraints	0	64	33.87	28.00	508	0	None	14.52	0.43	1.02
Separator variables	0	36	19.00	15.00	285	0	None	8.37	0.44	1.38
Clusters per var	1	7	4.96	6.00	357	MAX VALUE	106.59	1.79	0.36	1.55

Dual tree decomposition

Number of clusters: 64
Number of leaves: 32
Tree depth: 7
CIR: 0.39
Independent Cluster Pairs: 762
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/DualTree1.json

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

Cluster constraints 77 165 102.52 79.00 6,561 MAX VALUE 293.67 31.22 0.30 1.58

Variables per cluster 17 33 22.08 20.00 1,413 MAX VALUE 196.02 5.71 0.26 1.51

Separator constraints 0 90 62.02 63.00 3,969 0 None 25.56 0.41 1.16

Separator variables 0 25 17.44 16.00 1,116 0 None 4.92 0.28 1.34

Clusters per variable 1 31 4.76 5.00 1,413 MAX VALUE 402.44 4.25 0.89 1.72

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	77	165	102.52	79.00	6,561	MAX VALUE	293.67	31.22	0.30	1.58
Variables per cluster	17	33	22.08	20.00	1,413	MAX VALUE	196.02	5.71	0.26	1.51
Separator constraints	0	90	62.02	63.00	3,969	0	None	25.56	0.41	1.16
Separator variables	0	25	17.44	16.00	1,116	0	None	4.92	0.28	1.34
Clusters per variable	1	31	4.76	5.00	1,413	MAX VALUE	402.44	4.25	0.89	1.72

Primal graph

Density: 21.13%
MCB compute time (ms): 37
MCB cycles: 469
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/Primal1.json

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

Clustering coefficient 0.47 0.47 0.47 0.47 33.60 0.00 -54.87 0.00 0.00 0.00

Degree 15 15 15.00 15.00 1,080 MAX VALUE 194.98 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.12 3.00 1,463 MAX VALUE 531.36 0.32 0.10 0.37

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.47	0.47	0.47	33.60	0.00	-54.87	0.00	0.00	0.00
Degree	15	15	15.00	15.00	1,080	MAX VALUE	194.98	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.12	3.00	1,463	MAX VALUE	531.36	0.32	0.10	0.37

Triangulated primal graph

Density: 68.23%
MCB compute time (ms): 139
MCB cycles: 1,904
Triangles: None

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

Clustering coefficient 0.81 1.00 0.87 0.85 62.86 0.00 -9.93 0.06 0.07 2.32

Degree 15 61 48.44 56.00 3,488 MAX VALUE 273.58 15.50 0.32 2.16

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 5,712 MAX VALUE 2,091.76 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.81	1.00	0.87	0.85	62.86	0.00	-9.93	0.06	0.07	2.32
Degree	15	61	48.44	56.00	3,488	MAX VALUE	273.58	15.50	0.32	2.16
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	5,712	MAX VALUE	2,091.76	0.00	0.00	0.00

Dual graph

Density: 5.90%
MCB compute time (ms): 510
MCB cycles: 2,422
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/Dual1.json

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

Clustering coefficient 0.11 0.53 0.51 0.53 152.20 0.00 -205.35 0.07 0.14 0.14

Degree 16 64 17.45 16.00 5,184 MAX VALUE 835.93 8.23 0.47 0.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.04 3.00 7,371 MAX VALUE 2,691.05 0.20 0.07 0.18

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.11	0.53	0.51	0.53	152.20	0.00	-205.35	0.07	0.14	0.14
Degree	16	64	17.45	16.00	5,184	MAX VALUE	835.93	8.23	0.47	0.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.04	3.00	7,371	MAX VALUE	2,691.05	0.20	0.07	0.18

Minimal dual graph

Density: 1.31%
MCB compute time (ms): 140
MCB cycles: 280

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

Clustering coefficient 0.00 0.33 0.03 0.00 7.67 0.00 None 0.07 2.70 0.58

Degree 2 11 3.88 4.00 1,152 MAX VALUE 390.69 1.26 0.32 1.28

Eccentricity None None None None None None None None None None

MCB cycle size 3 8 4.96 5.00 1,389 MAX VALUE 442.49 1.00 0.20 1.32

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.03	0.00	7.67	0.00	None	0.07	2.70	0.58
Degree	2	11	3.88	4.00	1,152	MAX VALUE	390.69	1.26	0.32	1.28
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	8	4.96	5.00	1,389	MAX VALUE	442.49	1.00	0.20	1.32

Triangulated dual graph

Density: 13.62%
Triangles: 63,816

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

Clustering coefficient 0.16 1.00 0.87 0.86 257.77 0.00 -50.21 0.14 0.16 2.27

Degree 16 250 40.32 38.00 11,976 MAX VALUE 1,058.61 33.21 0.82 2.27

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	0.16	1.00	0.87	0.86	257.77	0.00	-50.21	0.14	0.16	2.27
Degree	16	250	40.32	38.00	11,976	MAX VALUE	1,058.61	33.21	0.82	2.27
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 3.72%

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

Clustering coefficient 0.15 1.00 0.74 0.71 219.24 0.00 -104.48 0.21 0.28 3.18

Degree 2 80 11.01 7.00 3,270 MAX VALUE 615.40 10.58 0.96 2.85

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	0.15	1.00	0.74	0.71	219.24	0.00	-104.48	0.21	0.28	3.18
Degree	2	80	11.01	7.00	3,270	MAX VALUE	615.40	10.58	0.96	2.85
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 0.95%
MCB compute time (ms): 108
MCB cycles: 280
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-08-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 9 3.51 2.00 1,296 MAX VALUE 376.54 2.86 0.81 0.60

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.40 6.00 1,792 MAX VALUE 517.80 0.80 0.12 0.50

XCSP 2.1 Benchmarks