XCSP 2.1 Benchmark Database

Instance: normalized-half-n25-d5-e56-r7-15
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: 294,713
Value tables: 563

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 12,257 250.15 62.00 73,720,900 MAX VALUE 1,174,310.00 711.02 2.84 5.46

Relational linkage 0.02 1.00 0.42 0.44 55,944.00 0.00 -122,606.00 0.12 0.30 4.61

Tightness 0.39 0.56 0.49 0.49 27.44 0.00 -40.08 0.03 0.07 4.03

Tuples 34,333 47,628 39,839.10 39,464.50 2,230,990 MAX VALUE 593.07 2,643.60 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 24 3.28 2.00 1,849 MAX VALUE 572.38 2.80 0.85 1.40

Value table partitions 5 15,623 237.25 125.00 133,573 MAX VALUE 2,473.71 792.38 3.34 1.23

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	12,257	250.15	62.00	73,720,900	MAX VALUE	1,174,310.00	711.02	2.84	5.46
Relational linkage	0.02	1.00	0.42	0.44	55,944.00	0.00	-122,606.00	0.12	0.30	4.61
Tightness	0.39	0.56	0.49	0.49	27.44	0.00	-40.08	0.03	0.07	4.03
Tuples	34,333	47,628	39,839.10	39,464.50	2,230,990	MAX VALUE	593.07	2,643.60	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	24	3.28	2.00	1,849	MAX VALUE	572.38	2.80	0.85	1.40
Value table partitions	5	15,623	237.25	125.00	133,573	MAX VALUE	2,473.71	792.38	3.34	1.23

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-r7-15/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/Tree1.json

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

Cluster constraints 35 44 39.50 39.50 79 1,540 7.34 4.50 0.11 0.69

Variables per cluster 23 24 23.50 23.50 47 552 6.31 0.50 0.02 0.69

Separator constraints 0 23 11.50 11.50 23 0 None 11.50 1.00 0.69

Separator variables 0 22 11.00 11.00 22 0 None 11.00 1.00 0.69

Clusters per var 1 2 1.88 2.00 47 4,194,300 15.25 0.32 0.17 0.37

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	35	44	39.50	39.50	79	1,540	7.34	4.50	0.11	0.69
Variables per cluster	23	24	23.50	23.50	47	552	6.31	0.50	0.02	0.69
Separator constraints	0	23	11.50	11.50	23	0	None	11.50	1.00	0.69
Separator variables	0	22	11.00	11.00	22	0	None	11.00	1.00	0.69
Clusters per var	1	2	1.88	2.00	47	4,194,300	15.25	0.32	0.17	0.37

Dual tree decomposition

Number of clusters: 5
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-r7-15/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/DualTree1.json

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

Cluster constraints 1,015 1,249 1,118.20 1,058.00 5,591 1.71e+15 35.07 106.98 0.10 1.61

Variables per cluster 47 52 49.20 48.00 246 286,711,000 19.47 2.32 0.05 1.05

Separator constraints 0 1,200 831.40 976.00 4,157 0 None 424.16 0.51 1.61

Separator variables 0 51 38.00 46.00 190 0 None 19.09 0.50 1.33

Clusters per variable 1 5 4.39 5.00 246 6.95e+34 80.23 1.05 0.24 1.02

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,015	1,249	1,118.20	1,058.00	5,591	1.71e+15	35.07	106.98	0.10	1.61
Variables per cluster	47	52	49.20	48.00	246	286,711,000	19.47	2.32	0.05	1.05
Separator constraints	0	1,200	831.40	976.00	4,157	0	None	424.16	0.51	1.61
Separator variables	0	51	38.00	46.00	190	0	None	19.09	0.50	1.33
Clusters per variable	1	5	4.39	5.00	246	6.95e+34	80.23	1.05	0.24	1.02

Primal graph

Density: 98.67%
MCB compute time (ms): 4
MCB cycles: 281
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/Primal1.json

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

Clustering coefficient 0.99 0.99 0.99 0.99 24.67 0.72 -0.34 0.00 0.00 0.86

Degree 22 24 23.68 24.00 592 2.27e+34 79.11 0.55 0.02 0.71

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 843 MAX VALUE 308.71 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.99	0.99	0.99	0.99	24.67	0.72	-0.34	0.00	0.00	0.86
Degree	22	24	23.68	24.00	592	2.27e+34	79.11	0.55	0.02	0.71
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	843	MAX VALUE	308.71	0.00	0.00	0.00

Triangulated primal graph

Density: 99.33%
MCB compute time (ms): 3
MCB cycles: 283
Triangles: None

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

Clustering coefficient 0.99 1.00 0.99 0.99 24.84 0.85 -0.16 0.00 0.00 0.37

Degree 22 24 23.84 24.00 596 2.69e+34 79.28 0.46 0.02 0.44

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 849 MAX VALUE 310.91 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.99	1.00	0.99	0.99	24.84	0.85	-0.16	0.00	0.00	0.37
Degree	22	24	23.84	24.00	596	2.69e+34	79.28	0.46	0.02	0.44
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	849	MAX VALUE	310.91	0.00	0.00	0.00

Dual graph

Density: 93.12%
MCB compute time (ms): 48
MCB cycles: 1,379
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/Dual1.json

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

Clustering coefficient 0.92 0.94 0.93 0.93 52.18 0.02 -3.96 0.00 0.00 3.63

Degree 46 55 51.21 51.00 2,868 MAX VALUE 220.38 1.94 0.04 1.97

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 4,137 MAX VALUE 1,514.99 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.92	0.94	0.93	0.93	52.18	0.02	-3.96	0.00	0.00	3.63
Degree	46	55	51.21	51.00	2,868	MAX VALUE	220.38	1.94	0.04	1.97
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	4,137	MAX VALUE	1,514.99	0.00	0.00	0.00

Minimal dual graph

Density: 21.36%
MCB compute time (ms): 9
MCB cycles: 436

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

Clustering coefficient 0.15 0.38 0.24 0.24 13.44 0.00 -80.82 0.04 0.18 3.53

Degree 8 16 11.75 12.00 658 MAX VALUE 137.31 1.81 0.15 1.96

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.43 3.00 1,494 MAX VALUE 532.44 0.50 0.15 0.70

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.15	0.38	0.24	0.24	13.44	0.00	-80.82	0.04	0.18	3.53
Degree	8	16	11.75	12.00	658	MAX VALUE	137.31	1.81	0.15	1.96
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.43	3.00	1,494	MAX VALUE	532.44	0.50	0.15	0.70

Triangulated dual graph

Density: 98.44%
Triangles: 26,526

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

Clustering coefficient 0.98 1.00 0.99 0.98 55.26 0.47 -0.75 0.00 0.00 1.09

Degree 46 55 54.14 55.00 3,032 MAX VALUE 223.49 1.94 0.04 1.04

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	0.98	1.00	0.99	0.98	55.26	0.47	-0.75	0.00	0.00	1.09
Degree	46	55	54.14	55.00	3,032	MAX VALUE	223.49	1.94	0.04	1.04
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 61.10%

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

Clustering coefficient 0.71 1.00 0.87 0.86 48.73 0.00 -8.03 0.08 0.09 3.46

Degree 8 49 33.61 41.00 1,882 MAX VALUE 189.16 13.76 0.41 2.82

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	0.71	1.00	0.87	0.86	48.73	0.00	-8.03	0.08	0.09	3.46
Degree	8	49	33.61	41.00	1,882	MAX VALUE	189.16	13.76	0.41	2.82
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 12.10%
MCB compute time (ms): 18
MCB cycles: 320
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/dag-half/normalized-half-n25-d5-e56-r7-15/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 24 9.68 7.00 784 MAX VALUE 177.23 4.41 0.46 1.29

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 1,280 MAX VALUE 443.61 0.00 0.00 0.00

XCSP 2.1 Benchmarks