XCSP 2.1 Benchmark Database

Instance: normalized-langford-2-13-ext
Number of variables: 26
Number of constraints: 325
Satisfiable: True
Timestamp: 2025-07-27 21:34:22
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 26
Number of constraints: 325

General features

Coarse blocks: 16,692
Value tables: 26

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

Arity 2 2 2.00 2.00 650 MAX VALUE 225.27 0.00 0.00 0.00

Coarse blocks size 1 25 24.33 25.00 406,068 MAX VALUE 52,223.00 3.96 0.16 0.13

Relational linkage 0.04 0.04 0.04 0.04 18.00 0.00 -1,524.79 0.00 0.00 0.00

Tightness 0.04 0.98 0.08 0.04 24.65 0.00 -1,016.88 0.18 2.42 0.27

Tuples 12 650 624.72 650.00 203,034 MAX VALUE 2,058.10 123.85 0.20 0.27

Values 26 26 26.00 26.00 676 6.16e+36 84.71 0.00 0.00 0.00

Value table constraints 25 25 25.00 25.00 650 2.22e+36 83.69 0.00 0.00 0.00

Value table partitions 26 26 26.00 26.00 676 6.16e+36 84.71 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	650	MAX VALUE	225.27	0.00	0.00	0.00
Coarse blocks size	1	25	24.33	25.00	406,068	MAX VALUE	52,223.00	3.96	0.16	0.13
Relational linkage	0.04	0.04	0.04	0.04	18.00	0.00	-1,524.79	0.00	0.00	0.00
Tightness	0.04	0.98	0.08	0.04	24.65	0.00	-1,016.88	0.18	2.42	0.27
Tuples	12	650	624.72	650.00	203,034	MAX VALUE	2,058.10	123.85	0.20	0.27
Values	26	26	26.00	26.00	676	6.16e+36	84.71	0.00	0.00	0.00
Value table constraints	25	25	25.00	25.00	650	2.22e+36	83.69	0.00	0.00	0.00
Value table partitions	26	26	26.00	26.00	676	6.16e+36	84.71	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/langford2ExtConvert/normalized-langford-2-13-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-ext/Tree1.json

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

Cluster constraints 325 325 325.00 325.00 325 325 5.78 0.00 0.00 0.00

Variables per cluster 26 26 26.00 26.00 26 26 3.26 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 26 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	325	325	325.00	325.00	325	325	5.78	0.00
Variables per cluster	26	26	26.00	26.00	26	26	3.26	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	26	1	0.00	0.00

Dual tree decomposition

Number of clusters: 24
Number of leaves: 13
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-ext/DualTree1.json

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

Cluster constraints 624 3,456 1,189.00 624.00 28,536 MAX VALUE 165.57 813.89 0.68 1.28

Variables per cluster 49 216 85.54 49.00 2,053 MAX VALUE 103.40 50.26 0.59 1.28

Separator constraints 0 2,016 864.00 576.00 20,736 0 None 465.38 0.54 1.28

Separator variables 0 168 72.00 48.00 1,728 0 None 38.78 0.54 1.28

Clusters per variable 1 8 6.32 7.00 2,053 MAX VALUE 575.73 1.80 0.28 1.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	624	3,456	1,189.00	624.00	28,536	MAX VALUE	165.57	813.89	0.68	1.28
Variables per cluster	49	216	85.54	49.00	2,053	MAX VALUE	103.40	50.26	0.59	1.28
Separator constraints	0	2,016	864.00	576.00	20,736	0	None	465.38	0.54	1.28
Separator variables	0	168	72.00	48.00	1,728	0	None	38.78	0.54	1.28
Clusters per variable	1	8	6.32	7.00	2,053	MAX VALUE	575.73	1.80	0.28	1.66

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 2,600
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-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 26.00 1.00 0.00 0.00 0.00 0.00

Degree 25 25 25.00 25.00 650 2.22e+36 83.69 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 26 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	26.00	1.00	0.00	0.00	0.00	0.00
Degree	25	25	25.00	25.00	650	2.22e+36	83.69	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	26	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: 2,600

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

Clustering coefficient 1.00 1.00 1.00 1.00 26.00 1.00 0.00 0.00 0.00 0.00

Degree 25 25 25.00 25.00 650 2.22e+36 83.69 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 26 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	26.00	1.00	0.00	0.00	0.00	0.00
Degree	25	25	25.00	25.00	650	2.22e+36	83.69	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	26	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: 14.81%
MCB compute time (ms): 3,275
MCB cycles: 7,476
Triangles: 62,400
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 165.96 0.00 -218.43 0.00 0.00 0.00

Degree 48 48 48.00 48.00 15,600 MAX VALUE 1,258.14 0.00 0.00 0.00

Eccentricity 2 2 2.00 2.00 650 MAX VALUE 225.27 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 22,428 MAX VALUE 8,213.23 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	165.96	0.00	-218.43
Degree	48	48	48.00	48.00	15,600	MAX VALUE	1,258.14
Eccentricity	2	2	2.00	2.00	650	MAX VALUE	225.27
MCB cycle size	3	3	3.00	3.00	22,428	MAX VALUE	8,213.23

Minimal dual graph

Density: 1.19%
MCB compute time (ms): 622
MCB cycles: 303

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 0.03 10.77 0.06

Degree 2 6 3.84 4.00 1,248 MAX VALUE 428.40 0.92 0.24 1.23

Eccentricity 7 12 9.48 9.00 3,080 MAX VALUE 729.19 0.96 0.10 1.36

MCB cycle size 3 13 5.91 6.00 1,791 MAX VALUE 532.20 1.17 0.20 1.43

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	0.03	10.77	0.06
Degree	2	6	3.84	4.00	1,248	MAX VALUE	428.40	0.92	0.24	1.23
Eccentricity	7	12	9.48	9.00	3,080	MAX VALUE	729.19	0.96	0.10	1.36
MCB cycle size	3	13	5.91	6.00	1,791	MAX VALUE	532.20	1.17	0.20	1.43

Triangulated dual graph

Density: 71.60%
Triangles: 2,728,960

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

Clustering coefficient 0.83 1.00 0.89 0.88 288.29 0.00 -39.48 0.05 0.06 2.41

Degree 48 289 232.00 261.00 75,400 MAX VALUE 1,746.64 68.34 0.29 2.41

Eccentricity 2 2 2.00 2.00 650 MAX VALUE 225.27 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.83	1.00	0.89	0.88	288.29	0.00	-39.48	0.05	0.06	2.41
Degree	48	289	232.00	261.00	75,400	MAX VALUE	1,746.64	68.34	0.29	2.41
Eccentricity	2	2	2.00	2.00	650	MAX VALUE	225.27	0.00	0.00	0.00

Triangulated minimal dual graph

Density: 9.36%

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

Clustering coefficient 0.47 1.00 0.81 0.76 262.23 0.00 -75.92 0.16 0.19 3.65

Degree 2 106 30.33 8.00 9,856 MAX VALUE 832.17 36.57 1.21 3.38

Eccentricity 3 5 3.84 4.00 1,249 MAX VALUE 433.81 0.57 0.15 0.86

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.81	0.76	262.23	0.00	-75.92	0.16	0.19	3.65
Degree	2	106	30.33	8.00	9,856	MAX VALUE	832.17	36.57	1.21	3.38
Eccentricity	3	5	3.84	4.00	1,249	MAX VALUE	433.81	0.57	0.15	0.86

Incidence graph

Density: 1.06%
MCB compute time (ms): 122
MCB cycles: 300
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford2ExtConvert/normalized-langford-2-13-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 25 3.70 2.00 1,300 MAX VALUE 308.96 6.02 1.63 0.26

Eccentricity 3 4 3.93 4.00 1,378 MAX VALUE 479.11 0.26 0.07 0.26

MCB cycle size 6 6 6.00 6.00 1,800 MAX VALUE 537.53 0.00 0.00 0.00

XCSP 2.1 Benchmarks