XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-16-250-350-21-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 10.42 10.00 83,380 MAX VALUE 18,606.90 1.91 0.18 2.06

Relational linkage 0.19 0.69 0.45 0.44 290.06 0.00 -516.23 0.08 0.17 1.60

Tightness 0.26 0.43 0.35 0.35 87.15 0.00 -264.33 0.03 0.08 3.35

Tuples 146 189 166.76 167.00 41,690 MAX VALUE 1,278.89 7.41 0.04 3.35

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

Value table constraints 8 19 12.50 13.00 500 MAX VALUE 100.05 2.77 0.22 2.06

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	10.42	10.00	83,380	MAX VALUE	18,606.90	1.91	0.18	2.06
Relational linkage	0.19	0.69	0.45	0.44	290.06	0.00	-516.23	0.08	0.17	1.60
Tightness	0.26	0.43	0.35	0.35	87.15	0.00	-264.33	0.03	0.08	3.35
Tuples	146	189	166.76	167.00	41,690	MAX VALUE	1,278.89	7.41	0.04	3.35
Values	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00
Value table constraints	8	19	12.50	13.00	500	MAX VALUE	100.05	2.77	0.22	2.06
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: 9
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/Tree1.json

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

Cluster constraints 16 111 49.69 32.50 795 3.60e+25 58.85 33.27 0.67 2.69

Variables per cluster 9 25 15.25 12.00 244 2.57e+18 42.39 6.01 0.39 2.17

Separator constraints 0 103 34.06 20.00 545 0 None 30.67 0.90 2.69

Separator variables 0 24 12.75 10.50 204 0 None 6.37 0.50 2.25

Clusters per var 1 12 6.10 7.00 244 1.56e+26 60.31 3.58 0.59 2.20

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	111	49.69	32.50	795	3.60e+25	58.85	33.27	0.67	2.69
Variables per cluster	9	25	15.25	12.00	244	2.57e+18	42.39	6.01	0.39	2.17
Separator constraints	0	103	34.06	20.00	545	0	None	30.67	0.90	2.69
Separator variables	0	24	12.75	10.50	204	0	None	6.37	0.50	2.25
Clusters per var	1	12	6.10	7.00	244	1.56e+26	60.31	3.58	0.59	2.20

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.11
Independent Cluster Pairs: 76
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/DualTree1.json

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

Cluster constraints 65 797 265.97 202.00 10,107 MAX VALUE 204.13 183.36 0.69 3.56

Variables per cluster 16 127 42.84 31.50 1,628 MAX VALUE 136.18 28.24 0.66 3.22

Separator constraints 0 425 186.29 161.00 7,079 0 None 105.54 0.57 3.56

Separator variables 0 95 36.26 28.00 1,378 0 None 21.31 0.59 3.23

Clusters per variable 1 10 6.51 7.00 1,628 MAX VALUE 435.86 2.50 0.38 2.11

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	65	797	265.97	202.00	10,107	MAX VALUE	204.13	183.36	0.69	3.56
Variables per cluster	16	127	42.84	31.50	1,628	MAX VALUE	136.18	28.24	0.66	3.22
Separator constraints	0	425	186.29	161.00	7,079	0	None	105.54	0.57	3.56
Separator variables	0	95	36.26	28.00	1,378	0	None	21.31	0.59	3.23
Clusters per variable	1	10	6.51	7.00	1,628	MAX VALUE	435.86	2.50	0.38	2.11

Primal graph

Density: 32.05%
MCB compute time (ms): 8
MCB cycles: 222
Triangles: 325
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/Primal1.json

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

Clustering coefficient 0.22 0.44 0.33 0.32 13.07 0.00 -45.14 0.05 0.14 3.35

Degree 8 19 12.50 13.00 500 MAX VALUE 100.05 2.77 0.22 2.06

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.04 3.00 674 MAX VALUE 246.19 0.19 0.06 0.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.22	0.44	0.33	0.32	13.07	0.00	-45.14	0.05	0.14	3.35
Degree	8	19	12.50	13.00	500	MAX VALUE	100.05	2.77	0.22	2.06
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.04	3.00	674	MAX VALUE	246.19	0.19	0.06	0.16

Triangulated primal graph

Density: 64.62%
MCB compute time (ms): 12
MCB cycles: 495
Triangles: 3,823

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

Clustering coefficient 0.71 1.00 0.87 0.84 34.71 0.00 -5.87 0.09 0.10 3.04

Degree 8 35 25.20 30.00 1,008 MAX VALUE 124.89 9.36 0.37 2.58

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,485 MAX VALUE 543.81 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	0.84	34.71	0.00	-5.87	0.09	0.10	3.04
Degree	8	35	25.20	30.00	1,008	MAX VALUE	124.89	9.36	0.37	2.58
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,485	MAX VALUE	543.81	0.00	0.00	0.00

Dual graph

Density: 9.73%
MCB compute time (ms): 612
MCB cycles: 3,746
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/Dual1.json

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

Clustering coefficient 0.47 0.58 0.51 0.50 126.77 0.00 -169.96 0.02 0.04 4.41

Degree 15 34 24.22 24.00 6,056 MAX VALUE 793.76 3.78 0.16 2.68

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.06 3.00 11,453 MAX VALUE 4,177.19 0.23 0.08 0.22

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.58	0.51	0.50	126.77	0.00	-169.96	0.02	0.04	4.41
Degree	15	34	24.22	24.00	6,056	MAX VALUE	793.76	3.78	0.16	2.68
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.06	3.00	11,453	MAX VALUE	4,177.19	0.23	0.08	0.22

Minimal dual graph

Density: 1.48%
MCB compute time (ms): 206
MCB cycles: 211

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

Clustering coefficient 0.00 0.33 0.00 0.00 1.17 0.00 None 0.03 7.26 0.15

Degree 2 6 3.68 4.00 920 MAX VALUE 319.04 0.85 0.23 1.21

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.73 7.00 1,419 MAX VALUE 398.83 1.11 0.16 1.46

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	1.17	0.00	None	0.03	7.26	0.15
Degree	2	6	3.68	4.00	920	MAX VALUE	319.04	0.85	0.23	1.21
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.73	7.00	1,419	MAX VALUE	398.83	1.11	0.16	1.46

Triangulated dual graph

Density: 52.32%
Triangles: 662,957

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

Clustering coefficient 0.72 1.00 0.84 0.82 210.93 0.00 -43.62 0.08 0.10 4.80

Degree 15 193 130.29 156.00 32,572 MAX VALUE 1,177.09 56.81 0.44 4.13

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	0.84	0.82	210.93	0.00	-43.62	0.08	0.10	4.80
Degree	15	193	130.29	156.00	32,572	MAX VALUE	1,177.09	56.81	0.44	4.13
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.18%

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

Clustering coefficient 0.51 1.00 0.82 0.78 204.51 0.00 -53.96 0.14 0.17 3.50

Degree 2 86 27.83 7.00 6,958 MAX VALUE 618.30 32.81 1.18 3.13

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	0.82	0.78	204.51	0.00	-53.96	0.14	0.17	3.50
Degree	2	86	27.83	7.00	6,958	MAX VALUE	618.30	32.81	1.18	3.13
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.19%
MCB compute time (ms): 79
MCB cycles: 211
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-21-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 19 3.45 2.00 1,000 MAX VALUE 273.34 3.76 1.09 0.69

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