XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-77-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:31
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 180

General features

Coarse blocks: 9,000
Value tables: 40

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

Arity 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00

Coarse blocks size 4 22 12.52 13.00 112,700 MAX VALUE 22,556.60 2.50 0.20 2.33

Relational linkage 0.16 0.56 0.36 0.36 359.28 0.00 -1,039.82 0.06 0.17 1.85

Tightness 0.44 0.55 0.50 0.50 89.84 0.00 -125.23 0.02 0.04 3.73

Tuples 280 350 313.06 313.50 56,350 MAX VALUE 1,034.21 12.45 0.04 3.73

Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Value table constraints 3 13 9.00 9.50 360 2.14e+37 85.96 2.52 0.28 2.21

Value table partitions 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	360	MAX VALUE	124.77	0.00	0.00	0.00
Coarse blocks size	4	22	12.52	13.00	112,700	MAX VALUE	22,556.60	2.50	0.20	2.33
Relational linkage	0.16	0.56	0.36	0.36	359.28	0.00	-1,039.82	0.06	0.17	1.85
Tightness	0.44	0.55	0.50	0.50	89.84	0.00	-125.23	0.02	0.04	3.73
Tuples	280	350	313.06	313.50	56,350	MAX VALUE	1,034.21	12.45	0.04	3.73
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	3	13	9.00	9.50	360	2.14e+37	85.96	2.52	0.28	2.21
Value table partitions	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00

Tree decomposition

Number of clusters: 21
Number of leaves: 10
Tree depth: 6
CIR: 0.14
Independent Cluster Pairs: 26
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/Tree1.json

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

Cluster constraints 3 59 24.71 20.00 519 6.43e+26 61.73 16.00 0.65 2.91

Variables per cluster 4 20 11.67 12.00 245 2.90e+21 49.42 4.98 0.43 2.40

Separator constraints 0 51 16.14 10.00 339 0 None 14.24 0.88 2.66

Separator variables 0 19 9.76 9.00 205 0 None 5.11 0.52 2.47

Clusters per var 1 13 6.12 6.50 245 2.89e+25 58.63 4.04 0.66 2.37

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	59	24.71	20.00	519	6.43e+26	61.73	16.00	0.65	2.91
Variables per cluster	4	20	11.67	12.00	245	2.90e+21	49.42	4.98	0.43	2.40
Separator constraints	0	51	16.14	10.00	339	0	None	14.24	0.88	2.66
Separator variables	0	19	9.76	9.00	205	0	None	5.11	0.52	2.47
Clusters per var	1	13	6.12	6.50	245	2.89e+25	58.63	4.04	0.66	2.37

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 6
CIR: 0.22
Independent Cluster Pairs: 149
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/DualTree1.json

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

Cluster constraints 18 337 126.05 107.00 4,790 MAX VALUE 175.32 82.94 0.66 3.60

Variables per cluster 8 83 28.97 22.50 1,101 MAX VALUE 121.30 18.67 0.64 3.14

Separator constraints 0 196 84.82 80.50 3,223 0 None 49.82 0.59 3.48

Separator variables 0 64 24.24 20.50 921 0 None 14.29 0.59 3.19

Clusters per variable 1 11 6.12 7.00 1,101 MAX VALUE 296.33 2.72 0.45 2.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	18	337	126.05	107.00	4,790	MAX VALUE	175.32	82.94	0.66	3.60
Variables per cluster	8	83	28.97	22.50	1,101	MAX VALUE	121.30	18.67	0.64	3.14
Separator constraints	0	196	84.82	80.50	3,223	0	None	49.82	0.59	3.48
Separator variables	0	64	24.24	20.50	921	0	None	14.29	0.59	3.19
Clusters per variable	1	11	6.12	7.00	1,101	MAX VALUE	296.33	2.72	0.45	2.26

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 156
Triangles: 135
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/Primal1.json

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

Clustering coefficient 0.00 0.48 0.25 0.25 10.15 0.00 None 0.09 0.36 3.40

Degree 3 13 9.00 9.50 360 2.14e+37 85.96 2.52 0.28 2.21

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.25 3.00 507 MAX VALUE 182.60 0.43 0.13 0.56

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.48	0.25	0.25	10.15	0.00	None	0.09	0.36	3.40
Degree	3	13	9.00	9.50	360	2.14e+37	85.96	2.52	0.28	2.21
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.25	3.00	507	MAX VALUE	182.60	0.43	0.13	0.56

Triangulated primal graph

Density: 50.64%
MCB compute time (ms): 10
MCB cycles: 365
Triangles: 2,312

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

Clustering coefficient 0.64 1.00 0.83 0.81 33.31 0.00 -7.67 0.11 0.13 3.04

Degree 3 31 19.75 24.50 790 MAX VALUE 112.34 9.25 0.47 2.92

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,095 MAX VALUE 400.99 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.64	1.00	0.83	0.81	33.31	0.00	-7.67	0.11	0.13	3.04
Degree	3	31	19.75	24.50	790	MAX VALUE	112.34	9.25	0.47	2.92
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,095	MAX VALUE	400.99	0.00	0.00	0.00

Dual graph

Density: 9.73%
MCB compute time (ms): 258
MCB cycles: 1,656
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/Dual1.json

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

Clustering coefficient 0.47 0.70 0.51 0.50 91.21 0.00 -122.70 0.03 0.06 4.11

Degree 7 24 17.41 18.00 3,134 MAX VALUE 510.83 3.19 0.18 2.52

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.18 3.00 5,260 MAX VALUE 1,901.43 0.42 0.13 0.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.70	0.51	0.50	91.21	0.00	-122.70	0.03	0.06	4.11
Degree	7	24	17.41	18.00	3,134	MAX VALUE	510.83	3.19	0.18	2.52
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.18	3.00	5,260	MAX VALUE	1,901.43	0.42	0.13	0.49

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 78
MCB cycles: 141

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 6 3.56 3.00 640 MAX VALUE 224.40 0.75 0.21 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.77 7.00 955 MAX VALUE 267.55 1.16 0.17 1.51

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	6	3.56	3.00	640	MAX VALUE	224.40	0.75	0.21	1.09
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.77	7.00	955	MAX VALUE	267.55	1.16	0.17	1.51

Triangulated dual graph

Density: 46.19%
Triangles: 193,312

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

Clustering coefficient 0.70 1.00 0.83 0.81 149.66 0.00 -34.28 0.09 0.11 4.59

Degree 7 131 82.69 98.50 14,884 MAX VALUE 759.07 40.26 0.49 3.91

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	0.70	1.00	0.83	0.81	149.66	0.00	-34.28	0.09	0.11	4.59
Degree	7	131	82.69	98.50	14,884	MAX VALUE	759.07	40.26	0.49	3.91
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.53%

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

Clustering coefficient 0.51 1.00 0.79 0.73 142.85 0.00 -45.30 0.16 0.20 3.27

Degree 2 63 20.63 7.00 3,714 MAX VALUE 420.68 22.57 1.09 3.02

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	0.51	1.00	0.79	0.73	142.85	0.00	-45.30	0.16	0.20	3.27
Degree	2	63	20.63	7.00	3,714	MAX VALUE	420.68	22.57	1.09	3.02
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 45
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-77-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 13 3.27 2.00 720 MAX VALUE 210.72 2.91 0.89 0.88

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.35 6.00 896 MAX VALUE 259.83 0.76 0.12 0.47

XCSP 2.1 Benchmarks