XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-16-250-350-54-ext
Number of variables: 40
Number of constraints: 250
Satisfiable: True
Timestamp: 2025-07-20 22:09:22
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 250

General features

Coarse blocks: 8,000
Value tables: 40

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

Arity 2 2 2.00 2.00 500 MAX VALUE 173.29 0.00 0.00 0.00

Coarse blocks size 3 16 10.36 10.00 82,894 MAX VALUE 18,558.20 1.91 0.18 2.06

Relational linkage 0.19 0.62 0.45 0.44 287.38 0.00 -522.49 0.08 0.17 1.61

Tightness 0.24 0.45 0.35 0.35 88.10 0.00 -261.68 0.03 0.09 3.34

Tuples 140 195 165.79 166.00 41,447 MAX VALUE 1,277.41 7.69 0.05 3.34

Values 16 16 16.00 16.00 640 MAX VALUE 110.90 0.00 0.00 0.00

Value table constraints 8 21 12.50 12.00 500 MAX VALUE 100.28 2.49 0.20 2.16

Value table partitions 16 16 16.00 16.00 640 MAX VALUE 110.90 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	500	MAX VALUE	173.29	0.00	0.00	0.00
Coarse blocks size	3	16	10.36	10.00	82,894	MAX VALUE	18,558.20	1.91	0.18	2.06
Relational linkage	0.19	0.62	0.45	0.44	287.38	0.00	-522.49	0.08	0.17	1.61
Tightness	0.24	0.45	0.35	0.35	88.10	0.00	-261.68	0.03	0.09	3.34
Tuples	140	195	165.79	166.00	41,447	MAX VALUE	1,277.41	7.69	0.05	3.34
Values	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00
Value table constraints	8	21	12.50	12.00	500	MAX VALUE	100.28	2.49	0.20	2.16
Value table partitions	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00

Tree decomposition

Number of clusters: 15
Number of leaves: 7
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/Tree1.json

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

Cluster constraints 17 112 47.60 40.00 714 1.46e+24 55.64 27.25 0.57 2.52

Variables per cluster 9 26 15.80 16.00 237 4.07e+17 40.55 5.33 0.34 2.34

Separator constraints 0 83 30.93 21.00 464 0 None 23.07 0.75 2.62

Separator variables 0 23 13.13 12.00 197 0 None 5.77 0.44 2.34

Clusters per var 1 12 5.92 6.50 237 3.76e+26 61.19 3.24 0.55 2.32

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	17	112	47.60	40.00	714	1.46e+24	55.64	27.25	0.57	2.52
Variables per cluster	9	26	15.80	16.00	237	4.07e+17	40.55	5.33	0.34	2.34
Separator constraints	0	83	30.93	21.00	464	0	None	23.07	0.75	2.62
Separator variables	0	23	13.13	12.00	197	0	None	5.77	0.44	2.34
Clusters per var	1	12	5.92	6.50	237	3.76e+26	61.19	3.24	0.55	2.32

Dual tree decomposition

Number of clusters: 38
Number of leaves: 18
Tree depth: 5
CIR: 0.10
Independent Cluster Pairs: 67
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/DualTree1.json

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

Cluster constraints 82 810 267.50 195.50 10,165 MAX VALUE 204.66 187.02 0.70 3.56

Variables per cluster 18 125 43.50 31.50 1,653 MAX VALUE 136.68 29.19 0.67 3.17

Separator constraints 0 445 188.58 156.50 7,166 0 None 108.08 0.57 3.46

Separator variables 0 99 36.92 29.00 1,403 0 None 22.24 0.60 3.22

Clusters per variable 1 10 6.61 7.00 1,653 MAX VALUE 439.46 2.53 0.38 2.09

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	82	810	267.50	195.50	10,165	MAX VALUE	204.66	187.02	0.70	3.56
Variables per cluster	18	125	43.50	31.50	1,653	MAX VALUE	136.68	29.19	0.67	3.17
Separator constraints	0	445	188.58	156.50	7,166	0	None	108.08	0.57	3.46
Separator variables	0	99	36.92	29.00	1,403	0	None	22.24	0.60	3.22
Clusters per variable	1	10	6.61	7.00	1,653	MAX VALUE	439.46	2.53	0.38	2.09

Primal graph

Density: 32.05%
MCB compute time (ms): 5
MCB cycles: 239
Triangles: 296
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/Primal1.json

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

Clustering coefficient 0.23 0.44 0.30 0.30 12.05 0.00 -48.41 0.04 0.15 3.35

Degree 8 21 12.50 12.00 500 MAX VALUE 100.28 2.49 0.20 2.16

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.07 3.00 734 MAX VALUE 267.46 0.26 0.08 0.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.23	0.44	0.30	0.30	12.05	0.00	-48.41	0.04	0.15	3.35
Degree	8	21	12.50	12.00	500	MAX VALUE	100.28	2.49	0.20	2.16
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.07	3.00	734	MAX VALUE	267.46	0.26	0.08	0.26

Triangulated primal graph

Density: 66.92%
MCB compute time (ms): 18
MCB cycles: 506
Triangles: 4,045

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

Clustering coefficient 0.71 1.00 0.87 0.85 34.66 0.00 -5.90 0.08 0.09 3.24

Degree 8 36 26.10 30.50 1,044 MAX VALUE 127.04 8.88 0.34 2.67

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,518 MAX VALUE 555.90 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.71	1.00	0.87	0.85	34.66	0.00	-5.90	0.08	0.09	3.24
Degree	8	36	26.10	30.50	1,044	MAX VALUE	127.04	8.88	0.34	2.67
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,518	MAX VALUE	555.90	0.00	0.00	0.00

Dual graph

Density: 9.64%
MCB compute time (ms): 1,288
MCB cycles: 3,160
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/Dual1.json

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

Clustering coefficient 0.48 0.59 0.50 0.50 125.72 0.00 -171.98 0.02 0.03 4.46

Degree 17 37 23.99 23.00 5,998 MAX VALUE 791.69 3.64 0.15 2.61

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.06 3.00 9,673 MAX VALUE 3,527.14 0.24 0.08 0.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.59	0.50	0.50	125.72	0.00	-171.98	0.02	0.03	4.46
Degree	17	37	23.99	23.00	5,998	MAX VALUE	791.69	3.64	0.15	2.61
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.06	3.00	9,673	MAX VALUE	3,527.14	0.24	0.08	0.23

Minimal dual graph

Density: 1.48%
MCB compute time (ms): 180
MCB cycles: 211

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 3.68 3.00 920 MAX VALUE 319.06 0.87 0.24 1.19

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.71 7.00 1,416 MAX VALUE 398.90 1.05 0.16 1.45

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	3.68	3.00	920	MAX VALUE	319.06	0.87	0.24	1.19
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.71	7.00	1,416	MAX VALUE	398.90	1.05	0.16	1.45

Triangulated dual graph

Density: 53.72%
Triangles: 702,262

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

Clustering coefficient 0.72 1.00 0.85 0.85 212.22 0.00 -42.03 0.08 0.09 4.72

Degree 17 203 133.76 154.00 33,440 MAX VALUE 1,184.22 57.39 0.43 4.10

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	0.72	1.00	0.85	0.85	212.22	0.00	-42.03	0.08	0.09	4.72
Degree	17	203	133.76	154.00	33,440	MAX VALUE	1,184.22	57.39	0.43	4.10
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 10.99%

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

Clustering coefficient 0.46 1.00 0.81 0.76 202.38 0.00 -56.78 0.14 0.18 3.49

Degree 2 87 27.37 7.50 6,842 MAX VALUE 621.21 31.81 1.16 3.18

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	0.46	1.00	0.81	0.76	202.38	0.00	-56.78	0.14	0.18	3.49
Degree	2	87	27.37	7.50	6,842	MAX VALUE	621.21	31.81	1.16	3.18
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.19%
MCB compute time (ms): 77
MCB cycles: 211
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-54-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 21 3.45 2.00 1,000 MAX VALUE 273.56 3.74 1.08 0.70

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.02 6.00 1,270 MAX VALUE 378.64 0.19 0.03 0.05

XCSP 2.1 Benchmarks