XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-11-ext
Number of variables: 33
Number of constraints: 528
Satisfiable: True
Timestamp: 2025-07-27 21:35:00
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 33
Number of constraints: 528

General features

Coarse blocks: 34,540
Value tables: 33

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

Arity 2 2 2.00 2.00 1,056 MAX VALUE 365.98 0.00 0.00 0.00

Coarse blocks size 1 32 30.97 32.00 1,069,820 MAX VALUE 115,742.00 5.55 0.18 0.15

Relational linkage 0.03 0.03 0.03 0.03 23.67 0.00 -2,730.77 0.00 0.00 0.00

Tightness 0.03 0.98 0.07 0.03 36.81 0.00 -1,769.76 0.19 2.71 0.27

Tuples 21 1,056 1,013.08 1,056.00 534,908 MAX VALUE 3,594.41 205.82 0.20 0.27

Values 33 33 33.00 33.00 1,089 MAX VALUE 115.39 0.00 0.00 0.00

Value table constraints 32 32 32.00 32.00 1,056 MAX VALUE 114.37 0.00 0.00 0.00

Value table partitions 33 33 33.00 33.00 1,089 MAX VALUE 115.39 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	1,056	MAX VALUE	365.98	0.00	0.00	0.00
Coarse blocks size	1	32	30.97	32.00	1,069,820	MAX VALUE	115,742.00	5.55	0.18	0.15
Relational linkage	0.03	0.03	0.03	0.03	23.67	0.00	-2,730.77	0.00	0.00	0.00
Tightness	0.03	0.98	0.07	0.03	36.81	0.00	-1,769.76	0.19	2.71	0.27
Tuples	21	1,056	1,013.08	1,056.00	534,908	MAX VALUE	3,594.41	205.82	0.20	0.27
Values	33	33	33.00	33.00	1,089	MAX VALUE	115.39	0.00	0.00	0.00
Value table constraints	32	32	32.00	32.00	1,056	MAX VALUE	114.37	0.00	0.00	0.00
Value table partitions	33	33	33.00	33.00	1,089	MAX VALUE	115.39	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/langford/normalized-langford-3-11-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-ext/Tree1.json

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

Cluster constraints 528 528 528.00 528.00 528 528 6.27 0.00 0.00 0.00

Variables per cluster 33 33 33.00 33.00 33 33 3.50 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 33 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	528	528	528.00	528.00	528	528	6.27	0.00
Variables per cluster	33	33	33.00	33.00	33	33	3.50	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	33	1	0.00	0.00

Dual tree decomposition

Number of clusters: 31
Number of leaves: 16
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-ext/DualTree1.json

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

Cluster constraints 1,023 7,060 2,089.00 1,023.00 64,759 MAX VALUE 230.29 1,622.45 0.78 1.46

Variables per cluster 63 344 117.74 63.00 3,650 MAX VALUE 142.56 78.54 0.67 1.46

Separator constraints 0 4,216 1,561.00 961.00 48,391 0 None 921.72 0.59 1.46

Separator variables 0 272 100.71 62.00 3,122 0 None 59.47 0.59 1.46

Clusters per variable 1 9 6.91 8.00 3,650 MAX VALUE 986.95 1.83 0.26 1.50

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,023	7,060	2,089.00	1,023.00	64,759	MAX VALUE	230.29	1,622.45	0.78	1.46
Variables per cluster	63	344	117.74	63.00	3,650	MAX VALUE	142.56	78.54	0.67	1.46
Separator constraints	0	4,216	1,561.00	961.00	48,391	0	None	921.72	0.59	1.46
Separator variables	0	272	100.71	62.00	3,122	0	None	59.47	0.59	1.46
Clusters per variable	1	9	6.91	8.00	3,650	MAX VALUE	986.95	1.83	0.26	1.50

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 5,456
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-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 33.00 1.00 0.00 0.00 0.00 0.00

Degree 32 32 32.00 32.00 1,056 MAX VALUE 114.37 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 33 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	33.00	1.00	0.00	0.00	0.00	0.00
Degree	32	32	32.00	32.00	1,056	MAX VALUE	114.37	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	33	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: 5,456

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

Clustering coefficient 1.00 1.00 1.00 1.00 33.00 1.00 0.00 0.00 0.00 0.00

Degree 32 32 32.00 32.00 1,056 MAX VALUE 114.37 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 33 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	33.00	1.00	0.00	0.00	0.00	0.00
Degree	32	32	32.00	32.00	1,056	MAX VALUE	114.37	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	33	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: 11.76%
MCB compute time (ms): 12,415
MCB cycles: 15,841
Triangles: 169,136
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 268.33 0.00 -357.40 0.00 0.00 0.00

Degree 62 62 62.00 62.00 32,736 MAX VALUE 2,179.13 0.00 0.00 0.00

Eccentricity 2 2 2.00 2.00 1,056 MAX VALUE 365.98 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 47,523 MAX VALUE 17,403.10 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	268.33	0.00	-357.40
Degree	62	62	62.00	62.00	32,736	MAX VALUE	2,179.13
Eccentricity	2	2	2.00	2.00	1,056	MAX VALUE	365.98
MCB cycle size	3	3	3.00	3.00	47,523	MAX VALUE	17,403.10

Minimal dual graph

Density: 0.74%
MCB compute time (ms): 2,749
MCB cycles: 496

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

Clustering coefficient 0.00 0.07 0.00 0.00 0.16 0.00 None 0.00 13.41 0.04

Degree 2 7 3.88 4.00 2,046 MAX VALUE 699.62 0.97 0.25 1.26

Eccentricity 8 13 10.16 10.00 5,362 MAX VALUE 1,221.66 0.93 0.09 1.35

MCB cycle size 3 10 6.03 6.00 2,990 MAX VALUE 878.91 1.29 0.21 1.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.07	0.00	0.00	0.16	0.00	None	0.00	13.41	0.04
Degree	2	7	3.88	4.00	2,046	MAX VALUE	699.62	0.97	0.25	1.26
Eccentricity	8	13	10.16	10.00	5,362	MAX VALUE	1,221.66	0.93	0.09	1.35
MCB cycle size	3	10	6.03	6.00	2,990	MAX VALUE	878.91	1.29	0.21	1.54

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: 7.69%

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

Clustering coefficient 0.51 1.00 0.81 0.76 426.44 0.00 -122.14 0.15 0.19 3.91

Degree 2 159 40.51 9.00 21,388 MAX VALUE 1,420.27 52.50 1.30 3.61

Eccentricity 3 6 4.39 4.00 2,320 MAX VALUE 775.82 0.64 0.14 0.97

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.51	1.00	0.81	0.76	426.44	0.00	-122.14	0.15	0.19	3.91
Degree	2	159	40.51	9.00	21,388	MAX VALUE	1,420.27	52.50	1.30	3.61
Eccentricity	3	6	4.39	4.00	2,320	MAX VALUE	775.82	0.64	0.14	0.97

Incidence graph

Density: 0.67%
MCB compute time (ms): 350
MCB cycles: 496
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford/normalized-langford-3-11-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 32 3.76 2.00 2,112 MAX VALUE 480.35 7.06 1.88 0.22

Eccentricity 3 4 3.94 4.00 2,211 MAX VALUE 768.22 0.24 0.06 0.22

MCB cycle size 6 6 6.00 6.00 2,976 MAX VALUE 888.71 0.00 0.00 0.00

XCSP 2.1 Benchmarks