XCSP 2.1 Benchmark Database

Instance: normalized-hole-09-ext
Number of variables: 90
Number of constraints: 415
Satisfiable: True
Timestamp: 2025-07-20 22:09:44
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 90
Number of constraints: 415

General features

Coarse blocks: 1,800
Value tables: 90

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

Arity 2 9 2.17 2.00 900 MAX VALUE 302.70 1.07 0.49 0.11

Coarse blocks size 1 256 26.90 2.00 48,420 MAX VALUE 1,559.23 76.20 2.83 1.02

Relational linkage 0.50 1.00 0.75 0.75 134.65 0.00 -62.74 0.25 0.33 0.69

Tightness 0.00 0.25 0.24 0.25 101.27 0.00 -623.83 0.04 0.16 0.11

Tuples 3 511 15.24 3.00 6,325 MAX VALUE 507.30 77.90 5.11 0.11

Values 2 2 2.00 2.00 180 1.24e+27 62.38 0.00 0.00 0.00

Value table constraints 10 10 10.00 10.00 900 MAX VALUE 207.23 0.00 0.00 0.00

Value table partitions 2 2 2.00 2.00 180 1.24e+27 62.38 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	9	2.17	2.00	900	MAX VALUE	302.70	1.07	0.49	0.11
Coarse blocks size	1	256	26.90	2.00	48,420	MAX VALUE	1,559.23	76.20	2.83	1.02
Relational linkage	0.50	1.00	0.75	0.75	134.65	0.00	-62.74	0.25	0.33	0.69
Tightness	0.00	0.25	0.24	0.25	101.27	0.00	-623.83	0.04	0.16	0.11
Tuples	3	511	15.24	3.00	6,325	MAX VALUE	507.30	77.90	5.11	0.11
Values	2	2	2.00	2.00	180	1.24e+27	62.38	0.00	0.00	0.00
Value table constraints	10	10	10.00	10.00	900	MAX VALUE	207.23	0.00	0.00	0.00
Value table partitions	2	2	2.00	2.00	180	1.24e+27	62.38	0.00	0.00	0.00

Tree decomposition

Number of clusters: 17
Number of leaves: 9
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/Tree1.json

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

Cluster constraints 45 161 70.47 46.00 1,198 4.43e+30 70.57 36.05 0.51 1.34

Variables per cluster 18 58 27.82 18.00 473 7.53e+23 54.98 12.94 0.47 1.34

Separator constraints 0 90 46.06 36.00 783 0 None 20.91 0.45 1.15

Separator variables 0 44 22.53 17.00 383 0 None 10.43 0.46 1.34

Clusters per var 1 7 5.26 6.00 473 MAX VALUE 138.82 1.85 0.35 1.59

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	45	161	70.47	46.00	1,198	4.43e+30	70.57	36.05	0.51	1.34
Variables per cluster	18	58	27.82	18.00	473	7.53e+23	54.98	12.94	0.47	1.34
Separator constraints	0	90	46.06	36.00	783	0	None	20.91	0.45	1.15
Separator variables	0	44	22.53	17.00	383	0	None	10.43	0.46	1.34
Clusters per var	1	7	5.26	6.00	473	MAX VALUE	138.82	1.85	0.35	1.59

Dual tree decomposition

Number of clusters: 81
Number of leaves: 45
Tree depth: 7
CIR: 0.41
Independent Cluster Pairs: 1,288
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/DualTree1.json

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

Cluster constraints 96 224 130.49 98.00 10,570 MAX VALUE 389.95 46.96 0.36 1.23

Variables per cluster 19 40 25.07 19.00 2,031 MAX VALUE 257.62 7.50 0.30 1.23

Separator constraints 0 120 80.49 80.00 6,520 0 None 32.96 0.41 0.86

Separator variables 0 30 19.95 18.00 1,616 0 None 5.84 0.29 1.23

Clusters per variable 1 36 4.89 5.00 2,031 MAX VALUE 578.28 4.59 0.94 1.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	96	224	130.49	98.00	10,570	MAX VALUE	389.95	46.96	0.36	1.23
Variables per cluster	19	40	25.07	19.00	2,031	MAX VALUE	257.62	7.50	0.30	1.23
Separator constraints	0	120	80.49	80.00	6,520	0	None	32.96	0.41	0.86
Separator variables	0	30	19.95	18.00	1,616	0	None	5.84	0.29	1.23
Clusters per variable	1	36	4.89	5.00	2,031	MAX VALUE	578.28	4.59	0.94	1.16

Primal graph

Density: 19.10%
MCB compute time (ms): 87
MCB cycles: 676
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-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 42.35 0.00 -67.84 0.00 0.00 0.00

Degree 17 17 17.00 17.00 1,530 MAX VALUE 254.99 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.11 3.00 2,100 MAX VALUE 763.38 0.31 0.10 0.34

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.47	0.47	0.47	42.35	0.00	-67.84	0.00	0.00	0.00
Degree	17	17	17.00	17.00	1,530	MAX VALUE	254.99	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.11	3.00	2,100	MAX VALUE	763.38	0.31	0.10	0.34

Triangulated primal graph

Density: 67.94%
MCB compute time (ms): 203
MCB cycles: 3,506
Triangles: None

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

Clustering coefficient 0.81 1.00 0.88 0.86 78.75 0.00 -12.20 0.06 0.07 2.34

Degree 17 77 60.47 69.00 5,442 MAX VALUE 361.48 19.63 0.32 2.34

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 10,518 MAX VALUE 3,851.73 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	0.88	0.86	78.75	0.00	-12.20	0.06	0.07	2.34
Degree	17	77	60.47	69.00	5,442	MAX VALUE	361.48	19.63	0.32	2.34
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	10,518	MAX VALUE	3,851.73	0.00	0.00	0.00

Dual graph

Density: 4.71%
MCB compute time (ms): 1,334
MCB cycles: 3,804
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/Dual1.json

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

Clustering coefficient 0.10 0.52 0.51 0.52 212.76 0.00 -285.63 0.06 0.13 0.11

Degree 18 81 19.52 18.00 8,100 MAX VALUE 1,214.55 9.66 0.49 0.11

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.04 3.00 11,548 MAX VALUE 4,218.25 0.19 0.06 0.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.10	0.52	0.51	0.52	212.76	0.00	-285.63	0.06	0.13	0.11
Degree	18	81	19.52	18.00	8,100	MAX VALUE	1,214.55	9.66	0.49	0.11
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.04	3.00	11,548	MAX VALUE	4,218.25	0.19	0.06	0.15

Minimal dual graph

Density: 0.94%
MCB compute time (ms): 398
MCB cycles: 396

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

Clustering coefficient 0.00 0.33 0.02 0.00 8.63 0.00 None 0.06 3.04 0.50

Degree 2 12 3.90 4.00 1,620 MAX VALUE 548.45 1.30 0.33 1.26

Eccentricity None None None None None None None None None None

MCB cycle size 3 8 5.07 5.00 2,009 MAX VALUE 634.27 1.05 0.21 1.34

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.02	0.00	8.63	0.00	None	0.06	3.04	0.50
Degree	2	12	3.90	4.00	1,620	MAX VALUE	548.45	1.30	0.33	1.26
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	8	5.07	5.00	2,009	MAX VALUE	634.27	1.05	0.21	1.34

Triangulated dual graph

Density: 11.68%
Triangles: 130,245

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

Clustering coefficient 0.14 1.00 0.87 0.87 361.85 0.00 -67.07 0.12 0.14 1.60

Degree 18 342 48.36 47.00 20,070 MAX VALUE 1,553.63 42.58 0.88 1.60

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	0.14	1.00	0.87	0.87	361.85	0.00	-67.07	0.12	0.14	1.60
Degree	18	342	48.36	47.00	20,070	MAX VALUE	1,553.63	42.58	0.88	1.60
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 2.95%

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

Clustering coefficient 0.12 1.00 0.75 0.68 309.51 0.00 -141.36 0.21 0.28 2.96

Degree 2 122 12.19 7.00 5,060 MAX VALUE 878.31 12.98 1.06 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	0.12	1.00	0.75	0.68	309.51	0.00	-141.36	0.21	0.28	2.96
Degree	2	122	12.19	7.00	5,060	MAX VALUE	878.31	12.98	1.06	2.85
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 0.71%
MCB compute time (ms): 239
MCB cycles: 396
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/varDimacs/normalized-hole-09-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 10 3.56 2.00 1,800 MAX VALUE 509.93 3.15 0.88 0.56

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.36 6.00 2,520 MAX VALUE 730.25 0.77 0.12 0.47

XCSP 2.1 Benchmarks