XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-16-250-350-43-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 10.37 10.00 82,972 MAX VALUE 18,568.90 1.89 0.18 2.06

Relational linkage 0.19 0.62 0.45 0.44 289.00 0.00 -517.56 0.07 0.16 1.55

Tightness 0.28 0.44 0.35 0.35 87.95 0.00 -262.05 0.03 0.08 3.33

Tuples 144 185 165.94 167.00 41,486 MAX VALUE 1,277.65 7.54 0.05 3.33

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

Value table constraints 8 17 12.50 13.00 500 MAX VALUE 100.21 2.45 0.20 2.15

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	10.37	10.00	82,972	MAX VALUE	18,568.90	1.89	0.18	2.06
Relational linkage	0.19	0.62	0.45	0.44	289.00	0.00	-517.56	0.07	0.16	1.55
Tightness	0.28	0.44	0.35	0.35	87.95	0.00	-262.05	0.03	0.08	3.33
Tuples	144	185	165.94	167.00	41,486	MAX VALUE	1,277.65	7.54	0.05	3.33
Values	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00
Value table constraints	8	17	12.50	13.00	500	MAX VALUE	100.21	2.45	0.20	2.15
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: 16
Number of leaves: 7
Tree depth: 4
CIR: 0.01
Independent Cluster Pairs: 1
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/Tree1.json

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

Cluster constraints 15 100 48.69 44.50 779 5.43e+25 59.26 27.92 0.57 2.69

Variables per cluster 9 25 15.62 15.00 250 4.37e+18 42.92 5.59 0.36 2.25

Separator constraints 0 84 33.06 30.00 529 0 None 25.49 0.77 2.77

Separator variables 0 23 13.12 12.50 210 0 None 6.07 0.46 2.25

Clusters per var 1 12 6.25 7.50 250 8.37e+26 61.99 3.60 0.58 2.32

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	15	100	48.69	44.50	779	5.43e+25	59.26	27.92	0.57	2.69
Variables per cluster	9	25	15.62	15.00	250	4.37e+18	42.92	5.59	0.36	2.25
Separator constraints	0	84	33.06	30.00	529	0	None	25.49	0.77	2.77
Separator variables	0	23	13.12	12.50	210	0	None	6.07	0.46	2.25
Clusters per var	1	12	6.25	7.50	250	8.37e+26	61.99	3.60	0.58	2.32

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 4
CIR: 0.11
Independent Cluster Pairs: 74
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/DualTree1.json

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

Cluster constraints 74 798 261.92 201.50 9,953 MAX VALUE 204.28 173.63 0.66 3.49

Variables per cluster 17 131 42.71 30.50 1,623 MAX VALUE 136.21 28.01 0.66 3.26

Separator constraints 0 432 183.10 163.00 6,958 0 None 99.91 0.55 3.48

Separator variables 0 93 36.13 27.50 1,373 0 None 21.19 0.59 3.25

Clusters per variable 1 9 6.49 7.00 1,623 MAX VALUE 434.02 2.54 0.39 1.98

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	74	798	261.92	201.50	9,953	MAX VALUE	204.28	173.63	0.66	3.49
Variables per cluster	17	131	42.71	30.50	1,623	MAX VALUE	136.21	28.01	0.66	3.26
Separator constraints	0	432	183.10	163.00	6,958	0	None	99.91	0.55	3.48
Separator variables	0	93	36.13	27.50	1,373	0	None	21.19	0.59	3.25
Clusters per variable	1	9	6.49	7.00	1,623	MAX VALUE	434.02	2.54	0.39	1.98

Primal graph

Density: 32.05%
MCB compute time (ms): 8
MCB cycles: 231
Triangles: 325
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/Primal1.json

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

Clustering coefficient 0.17 0.50 0.33 0.32 13.30 0.00 -44.76 0.06 0.19 3.40

Degree 8 17 12.50 13.00 500 MAX VALUE 100.21 2.45 0.20 2.15

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.03 3.00 701 MAX VALUE 256.08 0.18 0.06 0.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.17	0.50	0.33	0.32	13.30	0.00	-44.76	0.06	0.19	3.40
Degree	8	17	12.50	13.00	500	MAX VALUE	100.21	2.45	0.20	2.15
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.03	3.00	701	MAX VALUE	256.08	0.18	0.06	0.15

Triangulated primal graph

Density: 65.38%
MCB compute time (ms): 24
MCB cycles: 493
Triangles: 3,868

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

Clustering coefficient 0.73 1.00 0.86 0.85 34.57 0.00 -6.02 0.08 0.10 3.31

Degree 8 35 25.50 30.50 1,020 MAX VALUE 125.74 9.08 0.36 2.65

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,479 MAX VALUE 541.62 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.73	1.00	0.86	0.85	34.57	0.00	-6.02	0.08	0.10	3.31
Degree	8	35	25.50	30.50	1,020	MAX VALUE	125.74	9.08	0.36	2.65
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,479	MAX VALUE	541.62	0.00	0.00	0.00

Dual graph

Density: 9.62%
MCB compute time (ms): 1,746
MCB cycles: 3,033
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/Dual1.json

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

Clustering coefficient 0.47 0.57 0.50 0.50 125.89 0.00 -171.66 0.02 0.04 4.40

Degree 16 32 23.96 24.00 5,990 MAX VALUE 791.66 3.27 0.14 2.56

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.03 3.00 9,194 MAX VALUE 3,359.42 0.17 0.06 0.14

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.57	0.50	0.50	125.89	0.00	-171.66	0.02	0.04	4.40
Degree	16	32	23.96	24.00	5,990	MAX VALUE	791.66	3.27	0.14	2.56
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.03	3.00	9,194	MAX VALUE	3,359.42	0.17	0.06	0.14

Minimal dual graph

Density: 1.48%
MCB compute time (ms): 306
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 4.00 920 MAX VALUE 319.93 0.80 0.22 1.15

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.81 7.00 1,436 MAX VALUE 401.97 1.05 0.15 1.44

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	4.00	920	MAX VALUE	319.93	0.80	0.22	1.15
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.81	7.00	1,436	MAX VALUE	401.97	1.05	0.15	1.44

Triangulated dual graph

Density: 51.77%
Triangles: 652,560

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

Clustering coefficient 0.75 1.00 0.84 0.80 210.83 0.00 -43.70 0.08 0.10 4.75

Degree 16 183 128.90 171.00 32,226 MAX VALUE 1,173.43 57.19 0.44 3.64

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	0.75	1.00	0.84	0.80	210.83	0.00	-43.70	0.08	0.10	4.75
Degree	16	183	128.90	171.00	32,226	MAX VALUE	1,173.43	57.19	0.44	3.64
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.30%

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

Clustering coefficient 0.49 1.00 0.82 0.77 204.65 0.00 -53.79 0.14 0.17 3.43

Degree 2 90 28.14 8.00 7,036 MAX VALUE 623.54 32.80 1.17 3.19

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	0.49	1.00	0.82	0.77	204.65	0.00	-53.79	0.14	0.17	3.43
Degree	2	90	28.14	8.00	7,036	MAX VALUE	623.54	32.80	1.17	3.19
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.19%
MCB compute time (ms): 117
MCB cycles: 211
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-43-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 17 3.45 2.00 1,000 MAX VALUE 273.50 3.73 1.08 0.70

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.03 6.00 1,272 MAX VALUE 378.92 0.24 0.04 0.07

XCSP 2.1 Benchmarks