XCSP 2.1 Benchmark Database

Instance: normalized-half-n25-d5-e56-r7-5
Number of variables: 25
Number of constraints: 56
Satisfiable: True
Timestamp: 2025-07-15 13:00:07
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 25
Number of constraints: 56

General features

Coarse blocks: 265,638
Value tables: 559

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

Arity 7 7 7.00 7.00 392 MAX VALUE 108.97 0.00 0.00 0.00

Coarse blocks size 1 11,108 270.62 65.00 71,886,700 MAX VALUE 1,147,370.00 740.48 2.74 5.58

Relational linkage 0.02 1.00 0.42 0.44 51,366.10 0.00 -110,662.00 0.12 0.27 4.73

Tightness 0.42 0.56 0.50 0.50 27.98 0.00 -39.00 0.03 0.07 4.03

Tuples 34,030 45,403 39,091.20 38,719.50 2,189,110 MAX VALUE 591.99 2,732.24 0.07 4.03

Values 5 5 5.00 5.00 125 2.98e+17 40.24 0.00 0.00 0.00

Value table constraints 2 20 3.29 2.00 1,837 MAX VALUE 567.75 2.82 0.86 1.41

Value table partitions 5 3,125 218.70 125.00 122,252 MAX VALUE 2,460.82 473.02 2.16 1.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	7	7	7.00	7.00	392	MAX VALUE	108.97	0.00	0.00	0.00
Coarse blocks size	1	11,108	270.62	65.00	71,886,700	MAX VALUE	1,147,370.00	740.48	2.74	5.58
Relational linkage	0.02	1.00	0.42	0.44	51,366.10	0.00	-110,662.00	0.12	0.27	4.73
Tightness	0.42	0.56	0.50	0.50	27.98	0.00	-39.00	0.03	0.07	4.03
Tuples	34,030	45,403	39,091.20	38,719.50	2,189,110	MAX VALUE	591.99	2,732.24	0.07	4.03
Values	5	5	5.00	5.00	125	2.98e+17	40.24	0.00	0.00	0.00
Value table constraints	2	20	3.29	2.00	1,837	MAX VALUE	567.75	2.82	0.86	1.41
Value table partitions	5	3,125	218.70	125.00	122,252	MAX VALUE	2,460.82	473.02	2.16	1.24

Tree decomposition

Number of clusters: 2
Number of leaves: 1
Tree depth: 1
CIR: None
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/Tree1.json

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

Cluster constraints 40 43 41.50 41.50 83 1,720 7.45 1.50 0.04 0.69

Variables per cluster 24 24 24.00 24.00 48 576 6.36 0.00 0.00 0.00

Separator constraints 0 27 13.50 13.50 27 0 None 13.50 1.00 0.69

Separator variables 0 23 11.50 11.50 23 0 None 11.50 1.00 0.69

Clusters per var 1 2 1.92 2.00 48 8,388,610 15.94 0.27 0.14 0.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	40	43	41.50	41.50	83	1,720	7.45	1.50	0.04	0.69
Variables per cluster	24	24	24.00	24.00	48	576	6.36	0.00	0.00	0.00
Separator constraints	0	27	13.50	13.50	27	0	None	13.50	1.00	0.69
Separator variables	0	23	11.50	11.50	23	0	None	11.50	1.00	0.69
Clusters per var	1	2	1.92	2.00	48	8,388,610	15.94	0.27	0.14	0.28

Dual tree decomposition

Number of clusters: 4
Number of leaves: 2
Tree depth: 2
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/DualTree1.json

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

Cluster constraints 1,015 1,295 1,178.25 1,201.50 4,713 1.89e+12 28.27 106.66 0.09 1.39

Variables per cluster 47 53 50.50 51.00 202 6,476,600 15.68 2.29 0.05 1.39

Separator constraints 0 1,198 818.50 1,038.00 3,274 0 None 479.54 0.59 1.39

Separator variables 0 51 36.50 47.50 146 0 None 21.15 0.58 1.39

Clusters per variable 1 4 3.61 4.00 202 2.28e+30 69.90 0.75 0.21 0.81

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,015	1,295	1,178.25	1,201.50	4,713	1.89e+12	28.27	106.66	0.09	1.39
Variables per cluster	47	53	50.50	51.00	202	6,476,600	15.68	2.29	0.05	1.39
Separator constraints	0	1,198	818.50	1,038.00	3,274	0	None	479.54	0.59	1.39
Separator variables	0	51	36.50	47.50	146	0	None	21.15	0.58	1.39
Clusters per variable	1	4	3.61	4.00	202	2.28e+30	69.90	0.75	0.21	0.81

Primal graph

Density: 99.67%
MCB compute time (ms): 5
MCB cycles: 277
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/Primal1.json

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

Clustering coefficient 1.00 1.00 1.00 1.00 24.92 0.92 -0.08 0.00 0.00 0.28

Degree 23 24 23.92 24.00 598 2.94e+34 79.37 0.27 0.01 0.28

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 831 MAX VALUE 304.32 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	24.92	0.92	-0.08	0.00	0.00	0.28
Degree	23	24	23.92	24.00	598	2.94e+34	79.37	0.27	0.01	0.28
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	831	MAX VALUE	304.32	0.00	0.00	0.00

Triangulated primal graph

Density: 99.67%
MCB compute time (ms): 5
MCB cycles: 277
Triangles: None

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

Clustering coefficient 1.00 1.00 1.00 1.00 24.92 0.92 -0.08 0.00 0.00 0.28

Degree 23 24 23.92 24.00 598 2.94e+34 79.37 0.27 0.01 0.28

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 831 MAX VALUE 304.32 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	24.92	0.92	-0.08	0.00	0.00	0.28
Degree	23	24	23.92	24.00	598	2.94e+34	79.37	0.27	0.01	0.28
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	831	MAX VALUE	304.32	0.00	0.00	0.00

Dual graph

Density: 93.44%
MCB compute time (ms): 51
MCB cycles: 1,384
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/Dual1.json

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

Clustering coefficient 0.93 0.94 0.93 0.93 52.30 0.02 -3.83 0.00 0.00 3.56

Degree 46 54 51.39 52.00 2,878 MAX VALUE 220.59 1.52 0.03 1.67

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 4,152 MAX VALUE 1,520.48 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.93	0.94	0.93	0.93	52.30	0.02	-3.83	0.00	0.00	3.56
Degree	46	54	51.39	52.00	2,878	MAX VALUE	220.59	1.52	0.03	1.67
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	4,152	MAX VALUE	1,520.48	0.00	0.00	0.00

Minimal dual graph

Density: 20.71%
MCB compute time (ms): 11
MCB cycles: 327

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

Clustering coefficient 0.11 0.33 0.24 0.24 13.53 0.00 -80.64 0.05 0.19 3.25

Degree 9 15 11.39 11.00 638 MAX VALUE 135.79 1.46 0.13 1.74

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.30 3.00 1,078 MAX VALUE 387.15 0.46 0.14 0.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.11	0.33	0.24	0.24	13.53	0.00	-80.64	0.05	0.19	3.25
Degree	9	15	11.39	11.00	638	MAX VALUE	135.79	1.46	0.13	1.74
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.30	3.00	1,078	MAX VALUE	387.15	0.46	0.14	0.61

Triangulated dual graph

Density: 98.96%
Triangles: 26,912

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

Clustering coefficient 0.99 1.00 0.99 0.99 55.49 0.60 -0.51 0.00 0.00 0.95

Degree 46 55 54.43 55.00 3,048 MAX VALUE 223.80 1.50 0.03 0.87

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	0.99	1.00	0.99	0.99	55.49	0.60	-0.51	0.00	0.00	0.95
Degree	46	55	54.43	55.00	3,048	MAX VALUE	223.80	1.50	0.03	0.87
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 60.71%

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

Clustering coefficient 0.69 1.00 0.86 0.84 48.27 0.00 -8.58 0.08 0.10 3.56

Degree 9 49 33.39 40.50 1,870 MAX VALUE 189.34 13.40 0.40 2.86

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	0.86	0.84	48.27	0.00	-8.58	0.08	0.10	3.56
Degree	9	49	33.39	40.50	1,870	MAX VALUE	189.34	13.40	0.40	2.86
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 12.10%
MCB compute time (ms): 21
MCB cycles: 329
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-5/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 7 20 9.68 7.00 784 MAX VALUE 177.40 4.27 0.44 1.31

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 1,316 MAX VALUE 456.09 0.00 0.00 0.00

XCSP 2.1 Benchmarks