XCSP 2.1 Benchmark Database

Instance: normalized-ii-8a1-ext
Number of variables: 132
Number of constraints: 252
Satisfiable: True
Timestamp: 2025-07-20 22:08:48
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 132
Number of constraints: 252

General features

Coarse blocks: 1,740
Value tables: 150

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

Arity 2 8 2.31 2.00 582 MAX VALUE 193.74 1.28 0.55 0.30

Coarse blocks size 1 128 20.22 2.00 35,190 MAX VALUE 2,528.50 39.83 1.97 1.77

Relational linkage 0.50 1.00 0.81 0.99 447.00 0.00 -144.04 0.24 0.29 1.17

Tightness 0.00 0.25 0.24 0.25 59.30 0.00 -403.41 0.06 0.23 0.30

Tuples 3 255 15.10 3.00 3,804 MAX VALUE 335.25 53.65 3.55 0.30

Values 2 2 2.00 2.00 264 MAX VALUE 91.50 0.00 0.00 0.00

Value table constraints 2 9 4.12 3.00 618 MAX VALUE 192.02 2.27 0.55 1.76

Value table partitions 2 64 3.68 2.00 552 MAX VALUE 131.00 8.74 2.37 0.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	8	2.31	2.00	582	MAX VALUE	193.74	1.28	0.55	0.30
Coarse blocks size	1	128	20.22	2.00	35,190	MAX VALUE	2,528.50	39.83	1.97	1.77
Relational linkage	0.50	1.00	0.81	0.99	447.00	0.00	-144.04	0.24	0.29	1.17
Tightness	0.00	0.25	0.24	0.25	59.30	0.00	-403.41	0.06	0.23	0.30
Tuples	3	255	15.10	3.00	3,804	MAX VALUE	335.25	53.65	3.55	0.30
Values	2	2	2.00	2.00	264	MAX VALUE	91.50	0.00	0.00	0.00
Value table constraints	2	9	4.12	3.00	618	MAX VALUE	192.02	2.27	0.55	1.76
Value table partitions	2	64	3.68	2.00	552	MAX VALUE	131.00	8.74	2.37	0.49

Tree decomposition

Number of clusters: 91
Number of leaves: 39
Tree depth: 9
CIR: 0.64
Independent Cluster Pairs: 2,579
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/Tree1.json

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

Cluster constraints 0 8 3.30 3.00 300 0 None 2.15 0.65 1.92

Variables per cluster 4 17 8.58 9.00 781 MAX VALUE 183.72 4.40 0.51 2.01

Separator constraints 0 8 0.53 0.00 48 0 None 1.72 3.26 0.43

Separator variables 0 16 7.13 6.00 649 0 None 4.17 0.58 2.09

Clusters per var 1 21 5.92 3.00 781 MAX VALUE 165.98 5.78 0.98 2.27

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	8	3.30	3.00	300	0	None	2.15	0.65	1.92
Variables per cluster	4	17	8.58	9.00	781	MAX VALUE	183.72	4.40	0.51	2.01
Separator constraints	0	8	0.53	0.00	48	0	None	1.72	3.26	0.43
Separator variables	0	16	7.13	6.00	649	0	None	4.17	0.58	2.09
Clusters per var	1	21	5.92	3.00	781	MAX VALUE	165.98	5.78	0.98	2.27

Dual tree decomposition

Number of clusters: 124
Number of leaves: 54
Tree depth: 9
CIR: 0.69
Independent Cluster Pairs: 5,169
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/DualTree1.json

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

Cluster constraints 3 122 30.35 19.00 3,764 MAX VALUE 384.12 24.52 0.81 3.19

Variables per cluster 4 44 13.40 11.00 1,661 MAX VALUE 299.10 8.80 0.66 2.59

Separator constraints 0 63 19.93 13.00 2,471 0 None 17.08 0.86 3.13

Separator variables 0 32 11.36 10.00 1,409 0 None 7.33 0.65 2.55

Clusters per variable 1 29 6.59 7.00 1,661 MAX VALUE 377.33 5.87 0.89 2.31

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	122	30.35	19.00	3,764	MAX VALUE	384.12	24.52	0.81	3.19
Variables per cluster	4	44	13.40	11.00	1,661	MAX VALUE	299.10	8.80	0.66	2.59
Separator constraints	0	63	19.93	13.00	2,471	0	None	17.08	0.86	3.13
Separator variables	0	32	11.36	10.00	1,409	0	None	7.33	0.65	2.55
Clusters per variable	1	29	6.59	7.00	1,661	MAX VALUE	377.33	5.87	0.89	2.31

Primal graph

Density: 5.93%
MCB compute time (ms): 34
MCB cycles: 382
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/Primal1.json

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

Clustering coefficient 0.00 0.76 0.30 0.17 38.96 0.00 None 0.32 1.07 1.60

Degree 3 15 7.77 7.50 1,026 MAX VALUE 252.87 3.84 0.49 2.28

Eccentricity None None None None None None None None None None

MCB cycle size 3 10 3.76 3.00 1,435 MAX VALUE 490.26 1.28 0.34 1.05

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.76	0.30	0.17	38.96	0.00	None	0.32	1.07	1.60
Degree	3	15	7.77	7.50	1,026	MAX VALUE	252.87	3.84	0.49	2.28
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	10	3.76	3.00	1,435	MAX VALUE	490.26	1.28	0.34	1.05

Triangulated primal graph

Density: 12.26%
MCB compute time (ms): 37
MCB cycles: 1,015
Triangles: None

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

Clustering coefficient 0.38 1.00 0.80 0.83 105.99 0.00 -33.32 0.19 0.23 2.96

Degree 3 41 16.06 13.50 2,120 MAX VALUE 324.16 11.55 0.72 2.87

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 3,045 MAX VALUE 1,115.09 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.38	1.00	0.80	0.83	105.99	0.00	-33.32	0.19	0.23	2.96
Degree	3	41	16.06	13.50	2,120	MAX VALUE	324.16	11.55	0.72	2.87
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	3,045	MAX VALUE	1,115.09	0.00	0.00	0.00

Dual graph

Density: 4.09%
MCB compute time (ms): 179
MCB cycles: 1,300
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/Dual1.json

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

Clustering coefficient 0.00 0.78 0.50 0.49 125.08 0.00 None 0.13 0.27 2.56

Degree 3 14 10.26 11.00 2,586 MAX VALUE 572.64 3.00 0.29 2.24

Eccentricity None None None None None None None None None None

MCB cycle size 3 10 3.61 3.00 4,687 MAX VALUE 1,626.44 1.02 0.28 0.85

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.78	0.50	0.49	125.08	0.00	None	0.13	0.27	2.56
Degree	3	14	10.26	11.00	2,586	MAX VALUE	572.64	3.00	0.29	2.24
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	10	3.61	3.00	4,687	MAX VALUE	1,626.44	1.02	0.28	0.85

Minimal dual graph

Density: 1.33%
MCB compute time (ms): 129
MCB cycles: 169

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

Clustering coefficient 0.00 0.20 0.01 0.00 1.78 0.00 None 0.03 4.59 0.24

Degree 2 8 3.33 3.00 840 MAX VALUE 295.55 0.97 0.29 0.94

Eccentricity None None None None None None None None None None

MCB cycle size 3 12 6.64 7.00 1,122 MAX VALUE 313.70 1.74 0.26 1.82

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.20	0.01	0.00	1.78	0.00	None	0.03	4.59	0.24
Degree	2	8	3.33	3.00	840	MAX VALUE	295.55	0.97	0.29	0.94
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	12	6.64	7.00	1,122	MAX VALUE	313.70	1.74	0.26	1.82

Triangulated dual graph

Density: 14.12%
Triangles: 52,537

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

Clustering coefficient 0.44 1.00 0.82 0.82 207.75 0.00 -52.65 0.13 0.16 3.93

Degree 3 100 35.43 40.50 8,928 MAX VALUE 808.54 24.10 0.68 3.46

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	0.44	1.00	0.82	0.82	207.75	0.00	-52.65	0.13	0.16	3.93
Degree	3	100	35.43	40.50	8,928	MAX VALUE	808.54	24.10	0.68	3.46
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 5.35%

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

Clustering coefficient 0.29 1.00 0.76 0.70 192.37 0.00 -76.45 0.19 0.25 3.17

Degree 2 73 13.44 6.00 3,386 MAX VALUE 524.47 13.26 0.99 2.88

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	0.29	1.00	0.76	0.70	192.37	0.00	-76.45	0.19	0.25	3.17
Degree	2	73	13.44	6.00	3,386	MAX VALUE	524.47	13.26	0.99	2.88
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 0.79%
MCB compute time (ms): 168
MCB cycles: 203
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a1-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 3.03 2.00 1,164 MAX VALUE 373.28 1.96 0.65 1.20

Eccentricity None None None None None None None None None None

MCB cycle size 4 20 8.49 8.00 1,724 MAX VALUE 419.72 3.34 0.39 1.30

XCSP 2.1 Benchmarks