XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-12-ext
Number of variables: 36
Number of constraints: 630
Satisfiable: True
Timestamp: 2025-07-27 21:34:59
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 36
Number of constraints: 630

General features

Coarse blocks: 45,000
Value tables: 36

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

Arity 2 2 2.00 2.00 1,260 MAX VALUE 436.68 0.00 0.00 0.00

Coarse blocks size 1 35 33.97 35.00 1,528,490 MAX VALUE 155,127.00 5.84 0.17 0.14

Relational linkage 0.03 0.03 0.03 0.03 26.00 0.00 -3,354.17 0.00 0.00 0.00

Tightness 0.03 0.98 0.06 0.03 40.31 0.00 -2,172.15 0.18 2.84 0.26

Tuples 23 1,260 1,213.09 1,260.00 764,244 MAX VALUE 4,406.37 235.74 0.19 0.26

Values 36 36 36.00 36.00 1,296 MAX VALUE 129.01 0.00 0.00 0.00

Value table constraints 35 35 35.00 35.00 1,260 MAX VALUE 127.99 0.00 0.00 0.00

Value table partitions 36 36 36.00 36.00 1,296 MAX VALUE 129.01 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	1,260	MAX VALUE	436.68	0.00	0.00	0.00
Coarse blocks size	1	35	33.97	35.00	1,528,490	MAX VALUE	155,127.00	5.84	0.17	0.14
Relational linkage	0.03	0.03	0.03	0.03	26.00	0.00	-3,354.17	0.00	0.00	0.00
Tightness	0.03	0.98	0.06	0.03	40.31	0.00	-2,172.15	0.18	2.84	0.26
Tuples	23	1,260	1,213.09	1,260.00	764,244	MAX VALUE	4,406.37	235.74	0.19	0.26
Values	36	36	36.00	36.00	1,296	MAX VALUE	129.01	0.00	0.00	0.00
Value table constraints	35	35	35.00	35.00	1,260	MAX VALUE	127.99	0.00	0.00	0.00
Value table partitions	36	36	36.00	36.00	1,296	MAX VALUE	129.01	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-3-12-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-ext/Tree1.json

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

Cluster constraints 630 630 630.00 630.00 630 630 6.45 0.00 0.00 0.00

Variables per cluster 36 36 36.00 36.00 36 36 3.58 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 36 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	630	630	630.00	630.00	630	630	6.45	0.00
Variables per cluster	36	36	36.00	36.00	36	36	3.58	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	36	1	0.00	0.00

Dual tree decomposition

Number of clusters: 34
Number of leaves: 18
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-ext/DualTree1.json

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

Cluster constraints 1,224 9,376 2,570.00 1,224.00 87,380 MAX VALUE 259.01 2,092.47 0.81 1.25

Variables per cluster 69 416 132.65 69.00 4,510 MAX VALUE 159.83 93.56 0.71 1.25

Separator constraints 0 5,440 1,940.00 1,156.00 65,960 0 None 1,216.00 0.63 1.25

Separator variables 0 320 114.12 68.00 3,880 0 None 71.53 0.63 1.25

Clusters per variable 1 9 7.16 8.00 4,510 MAX VALUE 1,200.28 1.90 0.26 1.63

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,224	9,376	2,570.00	1,224.00	87,380	MAX VALUE	259.01	2,092.47	0.81	1.25
Variables per cluster	69	416	132.65	69.00	4,510	MAX VALUE	159.83	93.56	0.71	1.25
Separator constraints	0	5,440	1,940.00	1,156.00	65,960	0	None	1,216.00	0.63	1.25
Separator variables	0	320	114.12	68.00	3,880	0	None	71.53	0.63	1.25
Clusters per variable	1	9	7.16	8.00	4,510	MAX VALUE	1,200.28	1.90	0.26	1.63

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 7,140
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-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 36.00 1.00 0.00 0.00 0.00 0.00

Degree 35 35 35.00 35.00 1,260 MAX VALUE 127.99 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 36 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	36.00	1.00	0.00	0.00	0.00	0.00
Degree	35	35	35.00	35.00	1,260	MAX VALUE	127.99	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	36	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: 7,140

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

Clustering coefficient 1.00 1.00 1.00 1.00 36.00 1.00 0.00 0.00 0.00 0.00

Degree 35 35 35.00 35.00 1,260 MAX VALUE 127.99 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 36 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	36.00	1.00	0.00	0.00	0.00	0.00
Degree	35	35	35.00	35.00	1,260	MAX VALUE	127.99	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	36	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: 10.81%
MCB compute time (ms): 23,145
MCB cycles: 20,791
Triangles: 242,760
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 319.70 0.00 -427.35 0.00 0.00 0.00

Degree 68 68 68.00 68.00 42,840 MAX VALUE 2,658.29 0.00 0.00 0.00

Eccentricity 2 2 2.00 2.00 1,260 MAX VALUE 436.68 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 62,373 MAX VALUE 22,841.20 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	319.70	0.00	-427.35
Degree	68	68	68.00	68.00	42,840	MAX VALUE	2,658.29
Eccentricity	2	2	2.00	2.00	1,260	MAX VALUE	436.68
MCB cycle size	3	3	3.00	3.00	62,373	MAX VALUE	22,841.20

Minimal dual graph

Density: 0.62%
MCB compute time (ms): 3,303
MCB cycles: 596

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 15.03 0.03

Degree 2 7 3.89 4.00 2,448 MAX VALUE 837.24 0.95 0.25 1.25

Eccentricity 9 14 11.53 12.00 7,264 MAX VALUE 1,537.12 1.16 0.10 1.55

MCB cycle size 3 15 6.01 6.00 3,580 MAX VALUE 1,056.71 1.18 0.20 1.42

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	15.03	0.03
Degree	2	7	3.89	4.00	2,448	MAX VALUE	837.24	0.95	0.25	1.25
Eccentricity	9	14	11.53	12.00	7,264	MAX VALUE	1,537.12	1.16	0.10	1.55
MCB cycle size	3	15	6.01	6.00	3,580	MAX VALUE	1,056.71	1.18	0.20	1.42

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: 7.28%

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

Clustering coefficient 0.47 1.00 0.81 0.76 510.18 0.00 -143.73 0.15 0.19 3.96

Degree 2 189 45.82 9.00 28,866 MAX VALUE 1,723.23 61.33 1.34 3.73

Eccentricity 3 6 4.30 4.00 2,712 MAX VALUE 913.02 0.61 0.14 0.93

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.81	0.76	510.18	0.00	-143.73	0.15	0.19	3.96
Degree	2	189	45.82	9.00	28,866	MAX VALUE	1,723.23	61.33	1.34	3.73
Eccentricity	3	6	4.30	4.00	2,712	MAX VALUE	913.02	0.61	0.14	0.93

Incidence graph

Density: 0.57%
MCB compute time (ms): 598
MCB cycles: 595
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-12-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 35 3.78 2.00 2,520 MAX VALUE 564.67 7.46 1.97 0.21

Eccentricity 3 4 3.95 4.00 2,628 MAX VALUE 912.91 0.23 0.06 0.21

MCB cycle size 6 6 6.00 6.00 3,570 MAX VALUE 1,066.10 0.00 0.00 0.00

XCSP 2.1 Benchmarks