XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-80-103-800-5-ext
Number of variables: 40
Number of constraints: 103
Satisfiable: True
Timestamp: 2025-07-20 22:09:37
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 103

General features

Coarse blocks: 16,400
Value tables: 39

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

Arity 2 2 2.00 2.00 206 1.01e+31 71.39 0.00 0.00 0.00

Coarse blocks size 3 33 16.07 16.00 263,591 MAX VALUE 45,123.80 3.54 0.22 2.68

Relational linkage 0.04 0.28 0.15 0.15 472.20 0.00 -5,957.31 0.03 0.20 2.29

Tightness 0.79 0.81 0.80 0.80 82.31 0.00 -23.10 0.00 0.01 4.16

Tuples 1,210 1,352 1,285.81 1,284.00 132,438 MAX VALUE 737.36 30.90 0.02 4.16

Values 80 80 80.00 80.00 3,200 MAX VALUE 175.28 0.00 0.00 0.00

Value table constraints 2 11 5.26 5.00 205 1.19e+27 62.34 1.82 0.35 1.85

Value table partitions 80 80 80.00 80.00 3,120 MAX VALUE 170.90 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	206	1.01e+31	71.39	0.00	0.00	0.00
Coarse blocks size	3	33	16.07	16.00	263,591	MAX VALUE	45,123.80	3.54	0.22	2.68
Relational linkage	0.04	0.28	0.15	0.15	472.20	0.00	-5,957.31	0.03	0.20	2.29
Tightness	0.79	0.81	0.80	0.80	82.31	0.00	-23.10	0.00	0.01	4.16
Tuples	1,210	1,352	1,285.81	1,284.00	132,438	MAX VALUE	737.36	30.90	0.02	4.16
Values	80	80	80.00	80.00	3,200	MAX VALUE	175.28	0.00	0.00	0.00
Value table constraints	2	11	5.26	5.00	205	1.19e+27	62.34	1.82	0.35	1.85
Value table partitions	80	80	80.00	80.00	3,120	MAX VALUE	170.90	0.00	0.00	0.00

Tree decomposition

Number of clusters: 27
Number of leaves: 16
Tree depth: 4
CIR: 0.34
Independent Cluster Pairs: 109
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/Tree1.json

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

Cluster constraints 1 15 6.11 5.00 165 1.19e+19 43.92 3.72 0.61 2.16

Variables per cluster 2 14 6.67 6.00 180 8.67e+20 48.21 3.24 0.49 2.17

Separator constraints 0 12 2.30 1.00 62 0 None 3.36 1.47 1.66

Separator variables 0 12 5.19 4.00 140 0 None 3.08 0.59 2.17

Clusters per var 1 14 4.50 2.00 180 1.98e+18 42.13 3.86 0.86 1.97

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	15	6.11	5.00	165	1.19e+19	43.92	3.72	0.61	2.16
Variables per cluster	2	14	6.67	6.00	180	8.67e+20	48.21	3.24	0.49	2.17
Separator constraints	0	12	2.30	1.00	62	0	None	3.36	1.47	1.66
Separator variables	0	12	5.19	4.00	140	0	None	3.08	0.59	2.17
Clusters per var	1	14	4.50	2.00	180	1.98e+18	42.13	3.86	0.86	1.97

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.36
Independent Cluster Pairs: 243
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/DualTree1.json

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

Cluster constraints 9 78 31.66 27.00 1,203 MAX VALUE 124.30 19.69 0.62 3.21

Variables per cluster 5 39 14.50 11.50 551 MAX VALUE 96.10 8.42 0.58 2.86

Separator constraints 0 42 18.47 16.50 702 0 None 11.51 0.62 2.99

Separator variables 0 27 11.79 10.00 448 0 None 6.45 0.55 2.89

Clusters per variable 1 11 5.35 5.00 551 MAX VALUE 149.80 2.88 0.54 2.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	9	78	31.66	27.00	1,203	MAX VALUE	124.30	19.69	0.62	3.21
Variables per cluster	5	39	14.50	11.50	551	MAX VALUE	96.10	8.42	0.58	2.86
Separator constraints	0	42	18.47	16.50	702	0	None	11.51	0.62	2.99
Separator variables	0	27	11.79	10.00	448	0	None	6.45	0.55	2.89
Clusters per variable	1	11	5.35	5.00	551	MAX VALUE	149.80	2.88	0.54	2.24

Primal graph

Density: 13.21%
MCB compute time (ms): 3
MCB cycles: 65
Triangles: 17
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/Primal1.json

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

Clustering coefficient 0.00 0.33 None 0.10 None None None None None 2.36

Degree 1 11 5.15 5.00 206 1.19e+27 62.34 1.92 0.37 1.93

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.92 4.00 255 1.49e+38 87.90 0.66 0.17 0.99

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	None	0.10	None	None	None	None	None	2.36
Degree	1	11	5.15	5.00	206	1.19e+27	62.34	1.92	0.37	1.93
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.92	4.00	255	1.49e+38	87.90	0.66	0.17	0.99

Triangulated primal graph

Density: 29.62%
MCB compute time (ms): 6
MCB cycles: 192
Triangles: 785

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

Clustering coefficient 0.48 1.00 None 0.80 None None None None None 2.89

Degree 1 26 11.55 8.00 462 8.13e+36 84.99 8.03 0.70 2.74

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 576 MAX VALUE 210.93 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	1.00	None	0.80	None	None	None	None	None	2.89
Degree	1	26	11.55	8.00	462	8.13e+36	84.99	8.03	0.70	2.74
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	576	MAX VALUE	210.93	0.00	0.00	0.00

Dual graph

Density: 9.54%
MCB compute time (ms): 67
MCB cycles: 420
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/Dual1.json

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

Clustering coefficient 0.40 1.00 0.50 0.47 51.84 0.00 -71.86 0.08 0.17 3.16

Degree 4 16 9.73 10.00 1,002 MAX VALUE 230.65 2.56 0.26 2.28

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.22 3.00 1,352 MAX VALUE 486.29 0.54 0.17 0.56

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	1.00	0.50	0.47	51.84	0.00	-71.86	0.08	0.17	3.16
Degree	4	16	9.73	10.00	1,002	MAX VALUE	230.65	2.56	0.26	2.28
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.22	3.00	1,352	MAX VALUE	486.29	0.54	0.17	0.56

Minimal dual graph

Density: 3.16%
MCB compute time (ms): 16
MCB cycles: 64

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 4 3.22 3.00 332 MAX VALUE 118.48 0.62 0.19 0.93

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 7.03 7.00 450 MAX VALUE 123.93 1.10 0.16 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	4	3.22	3.00	332	MAX VALUE	118.48	0.62	0.19	0.93
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	7.03	7.00	450	MAX VALUE	123.93	1.10	0.16	1.44

Triangulated dual graph

Density: 35.39%
Triangles: 20,748

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

Clustering coefficient 0.60 1.00 0.80 0.80 82.79 0.00 -23.53 0.11 0.14 4.10

Degree 4 67 36.10 39.00 3,718 MAX VALUE 343.79 20.60 0.57 3.62

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	0.60	1.00	0.80	0.80	82.79	0.00	-23.53	0.11	0.14	4.10
Degree	4	67	36.10	39.00	3,718	MAX VALUE	343.79	20.60	0.57	3.62
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.34%

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

Clustering coefficient 0.50 1.00 0.76 0.69 78.23 0.00 -31.33 0.18 0.24 2.97

Degree 2 39 12.58 6.00 1,296 MAX VALUE 210.49 12.14 0.96 2.93

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	0.50	1.00	0.76	0.69	78.23	0.00	-31.33	0.18	0.24	2.97
Degree	2	39	12.58	6.00	1,296	MAX VALUE	210.49	12.14	0.96	2.93
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.03%
MCB compute time (ms): 19
MCB cycles: 64
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-5-ext/Incidence1.json

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

Clustering coefficient 0.00 0.00 None 0.00 None None None None None 0.59

Degree 1 11 2.88 2.00 412 MAX VALUE 133.74 1.74 0.60 1.06

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.81 8.00 500 MAX VALUE 130.65 1.31 0.17 0.98

XCSP 2.1 Benchmarks