XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-8-753-100-67-ext
Number of variables: 40
Number of constraints: 753
Satisfiable: True
Timestamp: 2025-07-27 21:31:24
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 40
Number of constraints: 753

General features

Coarse blocks: 12,048
Value tables: 40

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

Arity 2 2 2.00 2.00 1,506 MAX VALUE 521.94 0.00 0.00 0.00

Coarse blocks size 3 8 7.20 7.00 86,778 MAX VALUE 23,695.80 0.85 0.12 1.15

Relational linkage 0.38 0.75 0.64 0.62 204.00 0.00 -147.18 0.09 0.13 1.02

Tightness 0.02 0.22 0.10 0.09 75.05 0.00 -1,795.81 0.04 0.37 2.25

Tuples 50 63 57.62 58.00 43,389 MAX VALUE 3,051.96 2.34 0.04 2.25

Values 8 8 8.00 8.00 320 1.33e+36 83.18 0.00 0.00 0.00

Value table constraints 35 39 37.65 38.00 1,506 MAX VALUE 145.12 1.01 0.03 1.35

Value table partitions 8 8 8.00 8.00 320 1.33e+36 83.18 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	1,506	MAX VALUE	521.94	0.00	0.00	0.00
Coarse blocks size	3	8	7.20	7.00	86,778	MAX VALUE	23,695.80	0.85	0.12	1.15
Relational linkage	0.38	0.75	0.64	0.62	204.00	0.00	-147.18	0.09	0.13	1.02
Tightness	0.02	0.22	0.10	0.09	75.05	0.00	-1,795.81	0.04	0.37	2.25
Tuples	50	63	57.62	58.00	43,389	MAX VALUE	3,051.96	2.34	0.04	2.25
Values	8	8	8.00	8.00	320	1.33e+36	83.18	0.00	0.00	0.00
Value table constraints	35	39	37.65	38.00	1,506	MAX VALUE	145.12	1.01	0.03	1.35
Value table partitions	8	8	8.00	8.00	320	1.33e+36	83.18	0.00	0.00	0.00

Tree decomposition

Number of clusters: 3
Number of leaves: 2
Tree depth: 1
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/Tree1.json

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

Cluster constraints 610 682 645.67 645.00 1,937 268,333,000 19.41 29.40 0.05 1.10

Variables per cluster 36 38 37.00 37.00 111 50,616 10.83 0.82 0.02 1.10

Separator constraints 0 609 394.67 575.00 1,184 0 None 279.42 0.71 1.10

Separator variables 0 36 23.67 35.00 71 0 None 16.74 0.71 1.10

Clusters per var 1 3 2.77 3.00 111 1.78e+17 39.72 0.52 0.19 0.57

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	610	682	645.67	645.00	1,937	268,333,000	19.41	29.40	0.05	1.10
Variables per cluster	36	38	37.00	37.00	111	50,616	10.83	0.82	0.02	1.10
Separator constraints	0	609	394.67	575.00	1,184	0	None	279.42	0.71	1.10
Separator variables	0	36	23.67	35.00	71	0	None	16.74	0.71	1.10
Clusters per var	1	3	2.77	3.00	111	1.78e+17	39.72	0.52	0.19	0.57

Dual tree decomposition

Number of clusters: 38
Number of leaves: 20
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/DualTree1.json

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

Cluster constraints 1,220 11,720 3,024.97 1,520.00 114,949 MAX VALUE 295.27 2,547.25 0.84 2.87

Variables per cluster 69 488 146.08 77.00 5,551 MAX VALUE 181.86 107.56 0.74 2.55

Separator constraints 0 6,408 2,298.18 1,444.00 87,331 0 None 1,467.72 0.64 2.83

Separator variables 0 360 126.26 76.00 4,798 0 None 81.76 0.65 2.52

Clusters per variable 1 9 7.37 8.00 5,551 MAX VALUE 1,458.03 1.91 0.26 1.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,220	11,720	3,024.97	1,520.00	114,949	MAX VALUE	295.27	2,547.25	0.84	2.87
Variables per cluster	69	488	146.08	77.00	5,551	MAX VALUE	181.86	107.56	0.74	2.55
Separator constraints	0	6,408	2,298.18	1,444.00	87,331	0	None	1,467.72	0.64	2.83
Separator variables	0	360	126.26	76.00	4,798	0	None	81.76	0.65	2.52
Clusters per variable	1	9	7.37	8.00	5,551	MAX VALUE	1,458.03	1.91	0.26	1.52

Primal graph

Density: 96.54%
MCB compute time (ms): None
MCB cycles: None
Triangles: 8,884
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/Primal1.json

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

Clustering coefficient 0.96 0.97 0.97 0.96 38.60 0.24 -1.42 0.00 0.00 2.34

Degree 35 39 37.65 38.00 1,506 MAX VALUE 145.12 1.01 0.03 1.35

Eccentricity 1 2 1.80 2.00 72 4.29e+09 22.18 0.40 0.22 0.50

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	0.96	0.97	0.97	0.96	38.60	0.24	-1.42	0.00	0.00	2.34
Degree	35	39	37.65	38.00	1,506	MAX VALUE	145.12	1.01	0.03	1.35
Eccentricity	1	2	1.80	2.00	72	4.29e+09	22.18	0.40	0.22	0.50
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 99.23%
MCB compute time (ms): None
MCB cycles: None
Triangles: 9,661

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

Clustering coefficient 0.99 1.00 0.99 0.99 39.72 0.75 -0.29 0.00 0.00 0.65

Degree 35 39 38.70 39.00 1,548 MAX VALUE 146.22 0.81 0.02 0.60

Eccentricity 1 2 1.18 1.00 47 128 4.85 0.38 0.32 0.46

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	0.99	1.00	0.99	0.99	39.72	0.75	-0.29	0.00	0.00	0.65
Degree	35	39	38.70	39.00	1,548	MAX VALUE	146.22	0.81	0.02	0.60
Eccentricity	1	2	1.18	1.00	47	128	4.85	0.38	0.32	0.46
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 9.75%
MCB compute time (ms): 42,455
MCB cycles: 26,879
Triangles: 337,582
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 381.49 0.00 -512.03 0.00 0.00 2.13

Degree 68 76 73.35 73.00 55,236 MAX VALUE 3,234.23 1.39 0.02 1.72

Eccentricity 2 2 2.00 2.00 1,506 MAX VALUE 521.94 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 80,637 MAX VALUE 29,529.60 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.51	0.51	0.51	0.51	381.49	0.00	-512.03	0.00	0.00	2.13
Degree	68	76	73.35	73.00	55,236	MAX VALUE	3,234.23	1.39	0.02	1.72
Eccentricity	2	2	2.00	2.00	1,506	MAX VALUE	521.94	0.00	0.00	0.00
MCB cycle size	3	3	3.00	3.00	80,637	MAX VALUE	29,529.60	0.00	0.00	0.00

Minimal dual graph

Density: 0.52%
MCB compute time (ms): 9,739
MCB cycles: 715

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

Clustering coefficient 0.00 0.33 0.00 0.00 0.83 0.00 None 0.02 16.43 0.03

Degree 2 7 3.89 4.00 2,932 MAX VALUE 1,001.98 0.96 0.25 1.25

Eccentricity 9 15 11.68 12.00 8,794 MAX VALUE 1,847.25 1.11 0.10 1.52

MCB cycle size 3 16 6.17 6.00 4,411 MAX VALUE 1,284.80 1.30 0.21 1.59

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.83	0.00	None	0.02	16.43	0.03
Degree	2	7	3.89	4.00	2,932	MAX VALUE	1,001.98	0.96	0.25	1.25
Eccentricity	9	15	11.68	12.00	8,794	MAX VALUE	1,847.25	1.11	0.10	1.52
MCB cycle size	3	16	6.17	6.00	4,411	MAX VALUE	1,284.80	1.30	0.21	1.59

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: 6.72%

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

Clustering coefficient 0.47 1.00 0.81 0.77 612.91 0.00 -168.06 0.15 0.19 4.07

Degree 2 223 50.51 9.00 38,032 MAX VALUE 2,079.04 69.82 1.38 3.77

Eccentricity 3 6 4.29 4.00 3,228 MAX VALUE 1,088.32 0.60 0.14 0.91

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.81	0.77	612.91	0.00	-168.06	0.15	0.19	4.07
Degree	2	223	50.51	9.00	38,032	MAX VALUE	2,079.04	69.82	1.38	3.77
Eccentricity	3	6	4.29	4.00	3,228	MAX VALUE	1,088.32	0.60	0.14	0.91

Incidence graph

Density: 0.48%
MCB compute time (ms): 1,128
MCB cycles: 714
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-67-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 39 3.80 2.00 3,012 MAX VALUE 667.06 7.81 2.06 0.27

Eccentricity 3 5 4.05 4.00 3,210 MAX VALUE 1,107.29 0.26 0.06 0.28

MCB cycle size 6 6 6.00 6.00 4,284 MAX VALUE 1,279.32 0.00 0.00 0.00

XCSP 2.1 Benchmarks