XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-15-ext
Number of variables: 45
Number of constraints: 990
Satisfiable: True
Timestamp: 2025-07-27 21:34:59
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 45
Number of constraints: 990

General features

Coarse blocks: 88,560
Value tables: 45

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

Arity 2 2 2.00 2.00 1,980 MAX VALUE 686.22 0.00 0.00 0.00

Coarse blocks size 1 44 42.95 44.00 3,803,760 MAX VALUE 326,954.00 6.63 0.15 0.11

Relational linkage 0.02 0.02 0.02 0.02 33.00 0.00 -5,652.89 0.00 0.00 0.00

Tightness 0.02 0.99 0.05 0.02 50.80 0.00 -3,654.93 0.16 3.21 0.22

Tuples 29 1,980 1,921.09 1,980.00 1,901,880 MAX VALUE 7,394.50 333.24 0.17 0.22

Values 45 45 45.00 45.00 2,025 MAX VALUE 171.30 0.00 0.00 0.00

Value table constraints 44 44 44.00 44.00 1,980 MAX VALUE 170.29 0.00 0.00 0.00

Value table partitions 45 45 45.00 45.00 2,025 MAX VALUE 171.30 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	1,980	MAX VALUE	686.22	0.00	0.00	0.00
Coarse blocks size	1	44	42.95	44.00	3,803,760	MAX VALUE	326,954.00	6.63	0.15	0.11
Relational linkage	0.02	0.02	0.02	0.02	33.00	0.00	-5,652.89	0.00	0.00	0.00
Tightness	0.02	0.99	0.05	0.02	50.80	0.00	-3,654.93	0.16	3.21	0.22
Tuples	29	1,980	1,921.09	1,980.00	1,901,880	MAX VALUE	7,394.50	333.24	0.17	0.22
Values	45	45	45.00	45.00	2,025	MAX VALUE	171.30	0.00	0.00	0.00
Value table constraints	44	44	44.00	44.00	1,980	MAX VALUE	170.29	0.00	0.00	0.00
Value table partitions	45	45	45.00	45.00	2,025	MAX VALUE	171.30	0.00	0.00	0.00

Tree decomposition

Number of clusters: 1
Number of leaves: 1
Tree depth: 0
CIR: None
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/Tree1.json

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

Cluster constraints 990 990 990.00 990.00 990 990 6.90 0.00 0.00 0.00

Variables per cluster 45 45 45.00 45.00 45 45 3.81 0.00 0.00 0.00

Separator constraints 0 0 0.00 0.00 0 0 None 0.00 None 0.00

Separator variables 0 0 0.00 0.00 0 0 None 0.00 None 0.00

Clusters per var 1 1 1.00 1.00 45 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	990	990	990.00	990.00	990	990	6.90	0.00
Variables per cluster	45	45	45.00	45.00	45	45	3.81	0.00
Separator constraints	0	0	0.00	0.00	0	0	None	None
Separator variables	0	0	0.00	0.00	0	0	None	None
Clusters per var	1	1	1.00	1.00	45	1	0.00	0.00

Dual tree decomposition

Number of clusters: 43
Number of leaves: 22
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/DualTree1.json

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

Cluster constraints 1,935 17,620 4,351.00 1,935.00 187,093 MAX VALUE 348.62 3,939.68 0.91 1.46

Variables per cluster 87 632 179.35 87.00 7,712 MAX VALUE 213.63 141.99 0.79 1.46

Separator constraints 0 10,836 3,361.00 1,849.00 144,523 0 None 2,357.89 0.70 1.46

Separator variables 0 504 156.33 86.00 6,722 0 None 109.67 0.70 1.46

Clusters per variable 1 10 7.79 8.00 7,712 MAX VALUE 1,973.62 2.02 0.26 1.79

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,935	17,620	4,351.00	1,935.00	187,093	MAX VALUE	348.62	3,939.68	0.91	1.46
Variables per cluster	87	632	179.35	87.00	7,712	MAX VALUE	213.63	141.99	0.79	1.46
Separator constraints	0	10,836	3,361.00	1,849.00	144,523	0	None	2,357.89	0.70	1.46
Separator variables	0	504	156.33	86.00	6,722	0	None	109.67	0.70	1.46
Clusters per variable	1	10	7.79	8.00	7,712	MAX VALUE	1,973.62	2.02	0.26	1.79

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 14,190
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/Primal1.json

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

Clustering coefficient 1.00 1.00 1.00 1.00 45.00 1.00 0.00 0.00 0.00 0.00

Degree 44 44 44.00 44.00 1,980 MAX VALUE 170.29 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 45 1 0.00 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	1.00	1.00	1.00	1.00	45.00	1.00	0.00	0.00	0.00	0.00
Degree	44	44	44.00	44.00	1,980	MAX VALUE	170.29	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	45	1	0.00	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 14,190

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

Clustering coefficient 1.00 1.00 1.00 1.00 45.00 1.00 0.00 0.00 0.00 0.00

Degree 44 44 44.00 44.00 1,980 MAX VALUE 170.29 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 45 1 0.00 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	1.00	1.00	1.00	1.00	45.00	1.00	0.00	0.00	0.00	0.00
Degree	44	44	44.00	44.00	1,980	MAX VALUE	170.29	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	45	1	0.00	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 8.70%
MCB compute time (ms): 76,384
MCB cycles: 41,581
Triangles: 610,170
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 500.82 0.00 -674.64 0.00 0.00 0.00

Degree 86 86 86.00 86.00 85,140 MAX VALUE 4,409.80 0.00 0.00 0.00

Eccentricity 2 2 2.00 2.00 1,980 MAX VALUE 686.22 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 124,743 MAX VALUE 45,681.40 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)
Clustering coefficient	0.51	0.51	0.51	0.51	500.82	0.00	-674.64
Degree	86	86	86.00	86.00	85,140	MAX VALUE	4,409.80
Eccentricity	2	2	2.00	2.00	1,980	MAX VALUE	686.22
MCB cycle size	3	3	3.00	3.00	124,743	MAX VALUE	45,681.40

Minimal dual graph

Density: 0.40%
MCB compute time (ms): 14,528
MCB cycles: 950

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 18.85 0.02

Degree 2 7 3.91 4.00 3,870 MAX VALUE 1,321.00 0.97 0.25 1.26

Eccentricity 10 17 13.27 13.00 13,136 MAX VALUE 2,554.00 1.40 0.11 1.75

MCB cycle size 3 16 6.08 6.00 5,778 MAX VALUE 1,695.97 1.18 0.19 1.39

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	18.85	0.02
Degree	2	7	3.91	4.00	3,870	MAX VALUE	1,321.00	0.97	0.25	1.26
Eccentricity	10	17	13.27	13.00	13,136	MAX VALUE	2,554.00	1.40	0.11	1.75
MCB cycle size	3	16	6.08	6.00	5,778	MAX VALUE	1,695.97	1.18	0.19	1.39

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: 5.70%

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

Clustering coefficient 0.47 1.00 0.81 0.76 802.16 0.00 -225.59 0.15 0.19 4.14

Degree 2 267 56.41 9.00 55,850 MAX VALUE 2,763.27 82.07 1.45 3.84

Eccentricity 3 5 4.14 4.00 4,103 MAX VALUE 1,396.14 0.62 0.15 0.92

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.81	0.76	802.16	0.00	-225.59	0.15	0.19	4.14
Degree	2	267	56.41	9.00	55,850	MAX VALUE	2,763.27	82.07	1.45	3.84
Eccentricity	3	5	4.14	4.00	4,103	MAX VALUE	1,396.14	0.62	0.15	0.92

Incidence graph

Density: 0.37%
MCB compute time (ms): 1,490
MCB cycles: 946
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-15-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 44 3.83 2.00 3,960 MAX VALUE 856.50 8.57 2.24 0.18

Eccentricity 3 4 3.96 4.00 4,095 MAX VALUE 1,421.87 0.20 0.05 0.18

MCB cycle size 6 6 6.00 6.00 5,676 MAX VALUE 1,695.00 0.00 0.00 0.00

XCSP 2.1 Benchmarks