XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-85-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:31
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 180

General features

Coarse blocks: 9,000
Value tables: 40

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

Arity 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00

Coarse blocks size 2 21 12.46 12.00 112,142 MAX VALUE 22,510.70 2.50 0.20 2.33

Relational linkage 0.08 0.52 0.36 0.36 356.08 0.00 -1,049.23 0.06 0.17 1.84

Tightness 0.45 0.56 0.50 0.50 90.29 0.00 -124.36 0.02 0.04 3.80

Tuples 274 341 311.51 311.50 56,071 MAX VALUE 1,033.29 13.23 0.04 3.80

Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Value table constraints 4 15 9.00 9.00 360 2.36e+37 86.05 2.60 0.29 2.30

Value table partitions 25 25 25.00 25.00 1,000 MAX VALUE 128.75 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	360	MAX VALUE	124.77	0.00	0.00	0.00
Coarse blocks size	2	21	12.46	12.00	112,142	MAX VALUE	22,510.70	2.50	0.20	2.33
Relational linkage	0.08	0.52	0.36	0.36	356.08	0.00	-1,049.23	0.06	0.17	1.84
Tightness	0.45	0.56	0.50	0.50	90.29	0.00	-124.36	0.02	0.04	3.80
Tuples	274	341	311.51	311.50	56,071	MAX VALUE	1,033.29	13.23	0.04	3.80
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	15	9.00	9.00	360	2.36e+37	86.05	2.60	0.29	2.30
Value table partitions	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00

Tree decomposition

Number of clusters: 19
Number of leaves: 11
Tree depth: 3
CIR: 0.12
Independent Cluster Pairs: 18
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/Tree1.json

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

Cluster constraints 5 52 19.47 13.00 370 5.29e+22 52.32 13.75 0.71 2.58

Variables per cluster 5 21 10.68 9.00 203 6.48e+18 43.32 4.80 0.45 2.29

Separator constraints 0 37 10.00 6.00 190 0 None 10.37 1.04 2.55

Separator variables 0 19 8.58 7.00 163 0 None 4.49 0.52 2.36

Clusters per var 1 10 5.08 6.00 203 2.28e+22 51.48 3.33 0.66 2.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	52	19.47	13.00	370	5.29e+22	52.32	13.75	0.71	2.58
Variables per cluster	5	21	10.68	9.00	203	6.48e+18	43.32	4.80	0.45	2.29
Separator constraints	0	37	10.00	6.00	190	0	None	10.37	1.04	2.55
Separator variables	0	19	8.58	7.00	163	0	None	4.49	0.52	2.36
Clusters per var	1	10	5.08	6.00	203	2.28e+22	51.48	3.33	0.66	2.00

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 139
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/DualTree1.json

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

Cluster constraints 21 403 125.00 99.50 4,750 MAX VALUE 174.26 89.06 0.71 3.46

Variables per cluster 9 90 28.95 22.50 1,100 MAX VALUE 121.04 19.23 0.66 3.20

Separator constraints 0 225 83.55 72.00 3,175 0 None 53.86 0.64 3.46

Separator variables 0 63 24.21 20.00 920 0 None 14.73 0.61 3.20

Clusters per variable 1 10 6.11 7.00 1,100 MAX VALUE 295.71 2.74 0.45 2.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	21	403	125.00	99.50	4,750	MAX VALUE	174.26	89.06	0.71	3.46
Variables per cluster	9	90	28.95	22.50	1,100	MAX VALUE	121.04	19.23	0.66	3.20
Separator constraints	0	225	83.55	72.00	3,175	0	None	53.86	0.64	3.46
Separator variables	0	63	24.21	20.00	920	0	None	14.73	0.61	3.20
Clusters per variable	1	10	6.11	7.00	1,100	MAX VALUE	295.71	2.74	0.45	2.21

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 148
Triangles: 123
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/Primal1.json

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

Clustering coefficient 0.08 0.40 0.24 0.24 9.40 0.00 -60.15 0.07 0.31 3.33

Degree 4 15 9.00 9.00 360 2.36e+37 86.05 2.60 0.29 2.30

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.26 3.00 483 MAX VALUE 173.81 0.44 0.13 0.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.08	0.40	0.24	0.24	9.40	0.00	-60.15	0.07	0.31	3.33
Degree	4	15	9.00	9.00	360	2.36e+37	86.05	2.60	0.29	2.30
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.26	3.00	483	MAX VALUE	173.81	0.44	0.13	0.58

Triangulated primal graph

Density: 50.38%
MCB compute time (ms): 7
MCB cycles: 418
Triangles: 2,329

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

Clustering coefficient 0.68 1.00 0.84 0.82 33.63 0.00 -7.32 0.12 0.14 2.93

Degree 4 30 19.65 26.00 786 MAX VALUE 111.98 9.66 0.49 2.66

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,254 MAX VALUE 459.22 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.68	1.00	0.84	0.82	33.63	0.00	-7.32	0.12	0.14	2.93
Degree	4	30	19.65	26.00	786	MAX VALUE	111.98	9.66	0.49	2.66
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,254	MAX VALUE	459.22	0.00	0.00	0.00

Dual graph

Density: 9.78%
MCB compute time (ms): 273
MCB cycles: 1,863
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/Dual1.json

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

Clustering coefficient 0.45 0.64 0.51 0.50 91.25 0.00 -122.64 0.03 0.06 4.28

Degree 8 26 17.50 18.00 3,150 MAX VALUE 511.21 3.54 0.20 2.66

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.28 3.00 6,111 MAX VALUE 2,194.75 0.49 0.15 0.64

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.64	0.51	0.50	91.25	0.00	-122.64	0.03	0.06	4.28
Degree	8	26	17.50	18.00	3,150	MAX VALUE	511.21	3.54	0.20	2.66
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.28	3.00	6,111	MAX VALUE	2,194.75	0.49	0.15	0.64

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 80
MCB cycles: 141

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

Clustering coefficient 0.00 0.33 0.01 0.00 1.03 0.00 None 0.03 5.93 0.18

Degree 2 5 3.56 3.00 640 MAX VALUE 224.70 0.72 0.20 1.05

Eccentricity None None None None None None None None None None

MCB cycle size 3 10 6.75 7.00 952 MAX VALUE 266.47 1.26 0.19 1.60

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	1.03	0.00	None	0.03	5.93	0.18
Degree	2	5	3.56	3.00	640	MAX VALUE	224.70	0.72	0.20	1.05
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	10	6.75	7.00	952	MAX VALUE	266.47	1.26	0.19	1.60

Triangulated dual graph

Density: 47.16%
Triangles: 205,976

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

Clustering coefficient 0.73 1.00 0.84 0.80 150.75 0.00 -32.76 0.08 0.10 4.69

Degree 8 127 84.42 101.50 15,196 MAX VALUE 761.09 41.55 0.49 3.59

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	0.73	1.00	0.84	0.80	150.75	0.00	-32.76	0.08	0.10	4.69
Degree	8	127	84.42	101.50	15,196	MAX VALUE	761.09	41.55	0.49	3.59
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.51%

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

Clustering coefficient 0.51 1.00 0.79 0.72 142.83 0.00 -45.29 0.16 0.20 3.27

Degree 2 64 20.61 7.00 3,710 MAX VALUE 423.06 22.26 1.08 3.12

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	0.79	0.72	142.83	0.00	-45.29	0.16	0.20	3.27
Degree	2	64	20.61	7.00	3,710	MAX VALUE	423.06	22.26	1.08	3.12
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 42
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-85-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 15 3.27 2.00 720 MAX VALUE 210.82 2.92 0.89 0.89

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.45 6.00 910 MAX VALUE 261.84 0.84 0.13 0.54

XCSP 2.1 Benchmarks