XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-13-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:23
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 3 21 12.52 12.00 112,638 MAX VALUE 22,549.20 2.51 0.20 2.34

Relational linkage 0.12 0.64 0.36 0.36 357.08 0.00 -1,046.08 0.06 0.17 1.84

Tightness 0.44 0.56 0.50 0.50 89.89 0.00 -125.15 0.02 0.04 3.78

Tuples 272 352 312.88 313.00 56,319 MAX VALUE 1,034.09 13.26 0.04 3.78

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

Value table constraints 2 13 9.00 9.00 360 1.82e+37 85.79 2.58 0.29 2.20

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	3	21	12.52	12.00	112,638	MAX VALUE	22,549.20	2.51	0.20	2.34
Relational linkage	0.12	0.64	0.36	0.36	357.08	0.00	-1,046.08	0.06	0.17	1.84
Tightness	0.44	0.56	0.50	0.50	89.89	0.00	-125.15	0.02	0.04	3.78
Tuples	272	352	312.88	313.00	56,319	MAX VALUE	1,034.09	13.26	0.04	3.78
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	2	13	9.00	9.00	360	1.82e+37	85.79	2.58	0.29	2.20
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: 20
Number of leaves: 10
Tree depth: 4
CIR: 0.13
Independent Cluster Pairs: 22
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/Tree1.json

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

Cluster constraints 2 52 22.70 16.00 454 5.57e+24 56.98 15.51 0.68 2.65

Variables per cluster 3 20 10.95 9.00 219 6.40e+19 45.61 5.08 0.46 2.37

Separator constraints 0 39 13.70 7.50 274 0 None 13.17 0.96 2.46

Separator variables 0 18 8.95 7.50 179 0 None 4.98 0.56 2.44

Clusters per var 1 11 5.47 6.00 219 4.14e+23 54.38 3.51 0.64 2.04

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	52	22.70	16.00	454	5.57e+24	56.98	15.51	0.68	2.65
Variables per cluster	3	20	10.95	9.00	219	6.40e+19	45.61	5.08	0.46	2.37
Separator constraints	0	39	13.70	7.50	274	0	None	13.17	0.96	2.46
Separator variables	0	18	8.95	7.50	179	0	None	4.98	0.56	2.44
Clusters per var	1	11	5.47	6.00	219	4.14e+23	54.38	3.51	0.64	2.04

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.19
Independent Cluster Pairs: 125
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/DualTree1.json

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

Cluster constraints 38 379 124.82 104.50 4,743 MAX VALUE 176.10 83.33 0.67 3.53

Variables per cluster 12 87 28.92 22.50 1,099 MAX VALUE 121.68 18.58 0.64 3.06

Separator constraints 0 210 83.42 72.00 3,170 0 None 50.42 0.60 3.49

Separator variables 0 59 24.18 20.50 919 0 None 14.13 0.58 3.10

Clusters per variable 1 11 6.11 7.00 1,099 MAX VALUE 295.46 2.71 0.44 2.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	38	379	124.82	104.50	4,743	MAX VALUE	176.10	83.33	0.67	3.53
Variables per cluster	12	87	28.92	22.50	1,099	MAX VALUE	121.68	18.58	0.64	3.06
Separator constraints	0	210	83.42	72.00	3,170	0	None	50.42	0.60	3.49
Separator variables	0	59	24.18	20.50	919	0	None	14.13	0.58	3.10
Clusters per variable	1	11	6.11	7.00	1,099	MAX VALUE	295.46	2.71	0.44	2.16

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 149
Triangles: 124
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/Primal1.json

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

Clustering coefficient 0.00 0.40 0.24 0.24 9.65 0.00 None 0.07 0.30 3.18

Degree 2 13 9.00 9.00 360 1.82e+37 85.79 2.58 0.29 2.20

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.23 3.00 482 MAX VALUE 173.76 0.42 0.13 0.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.40	0.24	0.24	9.65	0.00	None	0.07	0.30	3.18
Degree	2	13	9.00	9.00	360	1.82e+37	85.79	2.58	0.29	2.20
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.23	3.00	482	MAX VALUE	173.76	0.42	0.13	0.55

Triangulated primal graph

Density: 49.74%
MCB compute time (ms): 10
MCB cycles: 363
Triangles: 2,271

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

Clustering coefficient 0.68 1.00 0.84 0.79 33.53 0.00 -7.41 0.11 0.13 2.99

Degree 2 30 19.40 24.50 776 MAX VALUE 110.88 9.50 0.49 2.71

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,089 MAX VALUE 398.80 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.68	1.00	0.84	0.79	33.53	0.00	-7.41	0.11	0.13	2.99
Degree	2	30	19.40	24.50	776	MAX VALUE	110.88	9.50	0.49	2.71
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,089	MAX VALUE	398.80	0.00	0.00	0.00

Dual graph

Density: 9.76%
MCB compute time (ms): 263
MCB cycles: 1,995
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/Dual1.json

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

Clustering coefficient 0.45 0.85 0.51 0.50 91.59 0.00 -122.16 0.04 0.09 4.14

Degree 11 24 17.48 18.00 3,146 MAX VALUE 511.99 3.11 0.18 2.51

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.34 3.00 6,655 MAX VALUE 2,381.12 0.52 0.16 0.71

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.85	0.51	0.50	91.59	0.00	-122.16	0.04	0.09	4.14
Degree	11	24	17.48	18.00	3,146	MAX VALUE	511.99	3.11	0.18	2.51
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.34	3.00	6,655	MAX VALUE	2,381.12	0.52	0.16	0.71

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 85
MCB cycles: 141

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

Clustering coefficient 0.00 0.17 0.00 0.00 0.37 0.00 None 0.02 7.94 0.10

Degree 2 5 3.56 3.50 640 MAX VALUE 224.78 0.70 0.20 1.05

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.75 7.00 952 MAX VALUE 266.81 1.18 0.17 1.50

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.37	0.00	None	0.02	7.94	0.10
Degree	2	5	3.56	3.50	640	MAX VALUE	224.78	0.70	0.20	1.05
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.75	7.00	952	MAX VALUE	266.81	1.18	0.17	1.50

Triangulated dual graph

Density: 46.29%
Triangles: 197,576

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

Clustering coefficient 0.69 1.00 0.84 0.80 150.45 0.00 -33.22 0.09 0.10 4.53

Degree 11 131 82.86 85.50 14,914 MAX VALUE 758.08 41.02 0.50 3.81

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	0.84	0.80	150.45	0.00	-33.22	0.09	0.10	4.53
Degree	11	131	82.86	85.50	14,914	MAX VALUE	758.08	41.02	0.50	3.81
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.74%

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

Clustering coefficient 0.52 1.00 0.80 0.75 144.04 0.00 -43.41 0.15 0.19 3.33

Degree 2 63 21.01 7.00 3,782 MAX VALUE 422.17 23.06 1.10 3.01

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	0.52	1.00	0.80	0.75	144.04	0.00	-43.41	0.15	0.19	3.33
Degree	2	63	21.01	7.00	3,782	MAX VALUE	422.17	23.06	1.10	3.01
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 46
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-13-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 210.56 2.92 0.89 0.85

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.38 6.00 900 MAX VALUE 260.41 0.79 0.12 0.49

XCSP 2.1 Benchmarks