XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-6-ext
Number of variables: 18
Number of constraints: 153
Satisfiable: True
Timestamp: 2025-07-20 22:08:33
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 18
Number of constraints: 153

General features

Coarse blocks: 5,400
Value tables: 18

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

Arity 2 2 2.00 2.00 306 MAX VALUE 106.05 0.00 0.00 0.00

Coarse blocks size 1 17 16.04 17.00 86,616 MAX VALUE 14,381.40 3.80 0.24 0.23

Relational linkage 0.06 0.06 0.06 0.06 12.00 0.00 -624.32 0.00 0.00 0.00

Tightness 0.06 0.97 0.13 0.06 19.33 0.00 -408.05 0.24 1.92 0.42

Tuples 11 306 283.06 306.00 43,308 MAX VALUE 838.16 78.64 0.28 0.42

Values 18 18 18.00 18.00 324 3.93e+22 52.03 0.00 0.00 0.00

Value table constraints 17 17 17.00 17.00 306 1.41e+22 51.00 0.00 0.00 0.00

Value table partitions 18 18 18.00 18.00 324 3.93e+22 52.03 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	306	MAX VALUE	106.05	0.00	0.00	0.00
Coarse blocks size	1	17	16.04	17.00	86,616	MAX VALUE	14,381.40	3.80	0.24	0.23
Relational linkage	0.06	0.06	0.06	0.06	12.00	0.00	-624.32	0.00	0.00	0.00
Tightness	0.06	0.97	0.13	0.06	19.33	0.00	-408.05	0.24	1.92	0.42
Tuples	11	306	283.06	306.00	43,308	MAX VALUE	838.16	78.64	0.28	0.42
Values	18	18	18.00	18.00	324	3.93e+22	52.03	0.00	0.00	0.00
Value table constraints	17	17	17.00	17.00	306	1.41e+22	51.00	0.00	0.00	0.00
Value table partitions	18	18	18.00	18.00	324	3.93e+22	52.03	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-3-6-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-ext/Tree1.json

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

Cluster constraints 153 153 153.00 153.00 153 153 5.03 0.00 0.00 0.00

Variables per cluster 18 18 18.00 18.00 18 18 2.89 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 18 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	153	153	153.00	153.00	153	153	5.03	0.00
Variables per cluster	18	18	18.00	18.00	18	18	2.89	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	18	1	0.00	0.00

Dual tree decomposition

Number of clusters: 16
Number of leaves: 9
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-ext/DualTree1.json

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

Cluster constraints 288 1,120 485.00 288.00 7,760 MAX VALUE 96.91 266.97 0.55 1.19

Variables per cluster 33 104 51.06 33.00 817 4.80e+26 61.44 23.60 0.46 1.19

Separator constraints 0 640 332.00 256.00 5,312 0 None 152.16 0.46 1.19

Separator variables 0 80 41.50 32.00 664 0 None 19.02 0.46 1.19

Clusters per variable 1 7 5.34 6.00 817 MAX VALUE 244.24 1.60 0.30 1.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	288	1,120	485.00	288.00	7,760	MAX VALUE	96.91	266.97	0.55	1.19
Variables per cluster	33	104	51.06	33.00	817	4.80e+26	61.44	23.60	0.46	1.19
Separator constraints	0	640	332.00	256.00	5,312	0	None	152.16	0.46	1.19
Separator variables	0	80	41.50	32.00	664	0	None	19.02	0.46	1.19
Clusters per variable	1	7	5.34	6.00	817	MAX VALUE	244.24	1.60	0.30	1.54

Primal graph

Density: 100.00%
MCB compute time (ms): 1
MCB cycles: 136
Triangles: 816
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-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 18.00 1.00 0.00 0.00 0.00 0.00

Degree 17 17 17.00 17.00 306 1.41e+22 51.00 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 408 MAX VALUE 149.41 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	18.00	1.00	0.00	0.00	0.00	0.00
Degree	17	17	17.00	17.00	306	1.41e+22	51.00	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	408	MAX VALUE	149.41	0.00	0.00	0.00

Triangulated primal graph

Density: 100.00%
MCB compute time (ms): 1
MCB cycles: 136
Triangles: 816

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

Clustering coefficient 1.00 1.00 1.00 1.00 18.00 1.00 0.00 0.00 0.00 0.00

Degree 17 17 17.00 17.00 306 1.41e+22 51.00 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 408 MAX VALUE 149.41 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	18.00	1.00	0.00	0.00	0.00	0.00
Degree	17	17	17.00	17.00	306	1.41e+22	51.00	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	408	MAX VALUE	149.41	0.00	0.00	0.00

Dual graph

Density: 21.05%
MCB compute time (ms): 144
MCB cycles: 2,296
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-ext/Dual1.json

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

Clustering coefficient 0.52 0.52 0.52 0.52 78.97 0.00 -101.19 0.00 0.00 0.00

Degree 32 32 32.00 32.00 4,896 MAX VALUE 530.26 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 6,888 MAX VALUE 2,522.41 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.52	0.52	0.52	0.52	78.97	0.00	-101.19	0.00	0.00	0.00
Degree	32	32	32.00	32.00	4,896	MAX VALUE	530.26	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	6,888	MAX VALUE	2,522.41	0.00	0.00	0.00

Minimal dual graph

Density: 2.48%
MCB compute time (ms): 37
MCB cycles: 139

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

Clustering coefficient 0.00 0.33 0.01 0.00 0.83 0.00 None 0.04 7.35 0.11

Degree 2 6 3.76 4.00 576 MAX VALUE 198.81 0.88 0.23 1.21

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 5.75 6.00 799 MAX VALUE 240.68 1.05 0.18 1.42

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	0.83	0.00	None	0.04	7.35	0.11
Degree	2	6	3.76	4.00	576	MAX VALUE	198.81	0.88	0.23	1.21
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	5.75	6.00	799	MAX VALUE	240.68	1.05	0.18	1.42

Triangulated dual graph

Density: 73.68%
Triangles: 295,808

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

Clustering coefficient 0.83 1.00 0.89 0.87 135.94 0.00 -18.33 0.05 0.06 2.07

Degree 32 137 112.00 129.00 17,136 MAX VALUE 713.00 30.64 0.27 2.07

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	0.83	1.00	0.89	0.87	135.94	0.00	-18.33	0.05	0.06	2.07
Degree	32	137	112.00	129.00	17,136	MAX VALUE	713.00	30.64	0.27	2.07
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 13.03%

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

Clustering coefficient 0.47 1.00 0.79 0.73 120.83 0.00 -39.41 0.16 0.21 3.34

Degree 2 62 19.80 9.00 3,030 MAX VALUE 364.76 20.05 1.01 3.14

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	0.47	1.00	0.79	0.73	120.83	0.00	-39.41	0.16	0.21	3.34
Degree	2	62	19.80	9.00	3,030	MAX VALUE	364.76	20.05	1.01	3.14
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.11%
MCB compute time (ms): 11
MCB cycles: 136
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-6-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 17 3.58 2.00 612 MAX VALUE 157.05 4.60 1.29 0.34

Eccentricity None None None None None None None None None None

MCB cycle size 6 6 6.00 6.00 816 MAX VALUE 243.68 0.00 0.00 0.00

XCSP 2.1 Benchmarks