XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-11-414-200-74-ext
Number of variables: 40
Number of constraints: 414
Satisfiable: True
Timestamp: 2025-07-27 21:29:59
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 40
Number of constraints: 414

General features

Coarse blocks: 9,108
Value tables: 40

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

Arity 2 2 2.00 2.00 828 MAX VALUE 286.96 0.00 0.00 0.00

Coarse blocks size 3 11 8.79 9.00 80,084 MAX VALUE 19,683.80 1.34 0.15 1.68

Relational linkage 0.27 0.73 0.55 0.55 243.82 0.00 -264.86 0.08 0.15 1.27

Tightness 0.11 0.31 0.20 0.20 83.07 0.00 -671.54 0.04 0.18 2.84

Tuples 83 108 96.72 97.00 40,042 MAX VALUE 1,892.32 4.30 0.04 2.84

Values 11 11 11.00 11.00 440 MAX VALUE 95.92 0.00 0.00 0.00

Value table constraints 15 27 20.70 20.50 828 MAX VALUE 120.83 2.84 0.14 2.37

Value table partitions 11 11 11.00 11.00 440 MAX VALUE 95.92 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	828	MAX VALUE	286.96	0.00	0.00	0.00
Coarse blocks size	3	11	8.79	9.00	80,084	MAX VALUE	19,683.80	1.34	0.15	1.68
Relational linkage	0.27	0.73	0.55	0.55	243.82	0.00	-264.86	0.08	0.15	1.27
Tightness	0.11	0.31	0.20	0.20	83.07	0.00	-671.54	0.04	0.18	2.84
Tuples	83	108	96.72	97.00	40,042	MAX VALUE	1,892.32	4.30	0.04	2.84
Values	11	11	11.00	11.00	440	MAX VALUE	95.92	0.00	0.00	0.00
Value table constraints	15	27	20.70	20.50	828	MAX VALUE	120.83	2.84	0.14	2.37
Value table partitions	11	11	11.00	11.00	440	MAX VALUE	95.92	0.00	0.00	0.00

Tree decomposition

Number of clusters: 11
Number of leaves: 5
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/Tree1.json

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

Cluster constraints 71 240 162.64 189.00 1,789 7.19e+23 54.93 66.76 0.41 2.40

Variables per cluster 16 30 24.18 27.00 266 1.22e+15 34.74 5.49 0.23 1.64

Separator constraints 0 220 125.00 89.00 1,375 0 None 73.71 0.59 2.40

Separator variables 0 29 20.55 19.00 226 0 None 8.31 0.40 1.85

Clusters per var 1 11 6.65 7.50 266 2.60e+29 67.73 3.08 0.46 2.12

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	71	240	162.64	189.00	1,789	7.19e+23	54.93	66.76	0.41	2.40
Variables per cluster	16	30	24.18	27.00	266	1.22e+15	34.74	5.49	0.23	1.64
Separator constraints	0	220	125.00	89.00	1,375	0	None	73.71	0.59	2.40
Separator variables	0	29	20.55	19.00	226	0	None	8.31	0.40	1.85
Clusters per var	1	11	6.65	7.50	266	2.60e+29	67.73	3.08	0.46	2.12

Dual tree decomposition

Number of clusters: 38
Number of leaves: 20
Tree depth: 4
CIR: 0.02
Independent Cluster Pairs: 13
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/DualTree1.json

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

Cluster constraints 245 2,974 852.45 557.50 32,393 MAX VALUE 247.07 692.69 0.81 3.53

Variables per cluster 31 248 77.26 51.00 2,936 MAX VALUE 157.79 55.82 0.72 3.31

Separator constraints 0 1,742 633.58 478.00 24,076 0 None 417.88 0.66 3.53

Separator variables 0 188 66.37 47.50 2,522 0 None 42.77 0.64 3.31

Clusters per variable 1 9 7.09 8.00 2,936 MAX VALUE 772.90 2.21 0.31 1.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	245	2,974	852.45	557.50	32,393	MAX VALUE	247.07	692.69	0.81	3.53
Variables per cluster	31	248	77.26	51.00	2,936	MAX VALUE	157.79	55.82	0.72	3.31
Separator constraints	0	1,742	633.58	478.00	24,076	0	None	417.88	0.66	3.53
Separator variables	0	188	66.37	47.50	2,522	0	None	42.77	0.64	3.31
Clusters per variable	1	9	7.09	8.00	2,936	MAX VALUE	772.90	2.21	0.31	1.61

Primal graph

Density: 53.08%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,455
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/Primal1.json

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

Clustering coefficient 0.47 0.60 0.53 0.52 21.01 0.00 -25.82 0.03 0.06 3.58

Degree 15 27 20.70 20.50 828 MAX VALUE 120.83 2.84 0.14 2.37

Eccentricity 2 2 2.00 2.00 80 1.10e+12 27.73 0.00 0.00 0.00

MCB cycle size 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	0.47	0.60	0.53	0.52	21.01	0.00	-25.82	0.03	0.06	3.58
Degree	15	27	20.70	20.50	828	MAX VALUE	120.83	2.84	0.14	2.37
Eccentricity	2	2	2.00	2.00	80	1.10e+12	27.73	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 84.74%
MCB compute time (ms): None
MCB cycles: None
Triangles: 6,648

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

Clustering coefficient 0.84 1.00 0.92 0.91 36.75 0.03 -3.44 0.05 0.05 3.13

Degree 15 39 33.05 35.50 1,322 MAX VALUE 138.86 6.50 0.20 2.28

Eccentricity 1 2 1.95 2.00 78 2.75e+11 26.34 0.22 0.11 0.20

MCB cycle size 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	0.84	1.00	0.92	0.91	36.75	0.03	-3.44	0.05	0.05	3.13
Degree	15	39	33.05	35.50	1,322	MAX VALUE	138.86	6.50	0.20	2.28
Eccentricity	1	2	1.95	2.00	78	2.75e+11	26.34	0.22	0.11	0.20
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 9.73%
MCB compute time (ms): 21,399
MCB cycles: 8,808
Triangles: 55,503
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/Dual1.json

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

Clustering coefficient 0.49 0.54 0.51 0.50 209.41 0.00 -282.21 0.01 0.01 4.96

Degree 30 51 40.18 40.00 16,634 MAX VALUE 1,527.05 3.92 0.10 2.77

Eccentricity 2 3 3.00 3.00 1,240 MAX VALUE 454.01 0.07 0.02 0.03

MCB cycle size 3 4 3.02 3.00 26,607 MAX VALUE 9,729.22 0.14 0.05 0.10

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.54	0.51	0.50	209.41	0.00	-282.21	0.01	0.01	4.96
Degree	30	51	40.18	40.00	16,634	MAX VALUE	1,527.05	3.92	0.10	2.77
Eccentricity	2	3	3.00	3.00	1,240	MAX VALUE	454.01	0.07	0.02	0.03
MCB cycle size	3	4	3.02	3.00	26,607	MAX VALUE	9,729.22	0.14	0.05	0.10

Minimal dual graph

Density: 0.92%
MCB compute time (ms): 1,720
MCB cycles: 375

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 3.81 4.00 1,576 MAX VALUE 542.57 0.89 0.23 1.20

Eccentricity 6 10 8.15 8.00 3,376 MAX VALUE 867.31 0.69 0.08 1.05

MCB cycle size 4 9 6.59 7.00 2,471 MAX VALUE 700.18 1.21 0.18 1.58

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	3.81	4.00	1,576	MAX VALUE	542.57	0.89	0.23	1.20
Eccentricity	6	10	8.15	8.00	3,376	MAX VALUE	867.31	0.69	0.08	1.05
MCB cycle size	4	9	6.59	7.00	2,471	MAX VALUE	700.18	1.21	0.18	1.58

Triangulated dual graph

Density: None%
Triangles: None

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

Clustering coefficient None None None None None None None None None None

Degree None None None None None None None None None None

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	None	None	None	None	None	None	None	None	None	None
Degree	None	None	None	None	None	None	None	None	None	None
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 10.07%

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

Clustering coefficient 0.57 1.00 0.83 0.79 343.06 0.00 -83.36 0.14 0.16 3.77

Degree 2 137 41.59 8.50 17,218 MAX VALUE 1,112.94 51.96 1.25 3.44

Eccentricity 3 5 3.74 4.00 1,549 MAX VALUE 542.24 0.51 0.14 0.74

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.57	1.00	0.83	0.79	343.06	0.00	-83.36	0.14	0.16	3.77
Degree	2	137	41.59	8.50	17,218	MAX VALUE	1,112.94	51.96	1.25	3.44
Eccentricity	3	5	3.74	4.00	1,549	MAX VALUE	542.24	0.51	0.14	0.74

Incidence graph

Density: 0.81%
MCB compute time (ms): 609
MCB cycles: 375
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.2/normalized-rand-2-40-11-414-200-74-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 27 3.65 2.00 1,656 MAX VALUE 407.79 5.37 1.47 0.51

Eccentricity 5 6 5.91 6.00 2,682 MAX VALUE 805.80 0.29 0.05 0.31

MCB cycle size 6 6 6.00 6.00 2,250 MAX VALUE 671.91 0.00 0.00 0.00

XCSP 2.1 Benchmarks