XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-words-vg12-13-ext
Number of variables: 156
Number of constraints: 25
Satisfiable: True
Timestamp: 2025-07-20 22:09:45
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 156
Number of constraints: 25

General features

Coarse blocks: 7,222
Value tables: 156

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

Arity 12 13 12.48 12.00 312 2.49e+27 63.08 0.50 0.04 0.69

Coarse blocks size 1 624 65.17 36.00 470,652 MAX VALUE 24,210.10 77.83 1.19 4.79

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -119,878.00 0.00 1.11 4.47

Tightness 1.00 1.00 1.00 1.00 25.00 1.00 -0.00 0.00 0.00 0.69

Tuples 1,136 1,881 1,523.40 1,881.00 38,085 MAX VALUE 182.44 372.20 0.24 0.69

Values 26 26 26.00 26.00 4,056 MAX VALUE 508.26 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 312 MAX VALUE 108.13 0.00 0.00 0.00

Value table partitions 18 26 24.88 25.00 3,881 MAX VALUE 501.16 1.29 0.05 1.42

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	12	13	12.48	12.00	312	2.49e+27	63.08	0.50	0.04	0.69
Coarse blocks size	1	624	65.17	36.00	470,652	MAX VALUE	24,210.10	77.83	1.19	4.79
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-119,878.00	0.00	1.11	4.47
Tightness	1.00	1.00	1.00	1.00	25.00	1.00	-0.00	0.00	0.00	0.69
Tuples	1,136	1,881	1,523.40	1,881.00	38,085	MAX VALUE	182.44	372.20	0.24	0.69
Values	26	26	26.00	26.00	4,056	MAX VALUE	508.26	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	312	MAX VALUE	108.13	0.00	0.00	0.00
Value table partitions	18	26	24.88	25.00	3,881	MAX VALUE	501.16	1.29	0.05	1.42

Tree decomposition

Number of clusters: 23
Number of leaves: 12
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/Tree1.json

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

Cluster constraints 0 2 1.09 2.00 25 0 None 0.97 0.90 0.84

Variables per cluster 24 98 40.83 24.00 939 5.77e+35 82.34 23.04 0.56 1.43

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

Separator variables 0 78 34.04 23.00 783 0 None 17.98 0.53 1.43

Clusters per var 1 8 6.02 7.00 939 MAX VALUE 263.24 2.02 0.34 1.74

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.09	2.00	25	0	None	0.97	0.90	0.84
Variables per cluster	24	98	40.83	24.00	939	5.77e+35	82.34	23.04	0.56	1.43
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	78	34.04	23.00	783	0	None	17.98	0.53	1.43
Clusters per var	1	8	6.02	7.00	939	MAX VALUE	263.24	2.02	0.34	1.74

Dual tree decomposition

Number of clusters: 13
Number of leaves: 2
Tree depth: 6
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/DualTree1.json

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

Cluster constraints 12 12 12.00 12.00 156 1.07e+14 32.30 0.00 0.00 0.00

Variables per cluster 13 13 13.00 13.00 169 3.03e+14 33.34 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 12 11.08 12.00 144 0 None 3.20 0.29 0.27

Clusters per variable 1 13 6.76 1.00 169 2.33e+13 30.78 6.00 0.89 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	12	12	12.00	12.00	156	1.07e+14	32.30	0.00	0.00	0.00
Variables per cluster	13	13	13.00	13.00	169	3.03e+14	33.34	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	12	11.08	12.00	144	0	None	3.20	0.29	0.27
Clusters per variable	1	13	6.76	1.00	169	2.33e+13	30.78	6.00	0.89	0.69

Primal graph

Density: 14.84%
MCB compute time (ms): 601
MCB cycles: 1,639
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/Primal1.json

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

Clustering coefficient 0.48 0.48 0.48 0.48 74.61 0.00 -115.06 0.00 0.00 0.00

Degree 23 23 23.00 23.00 3,588 MAX VALUE 489.14 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.08 3.00 5,049 MAX VALUE 1,838.60 0.27 0.09 0.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.48	0.48	0.48	74.61	0.00	-115.06	0.00	0.00	0.00
Degree	23	23	23.00	23.00	3,588	MAX VALUE	489.14	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.08	3.00	5,049	MAX VALUE	1,838.60	0.27	0.09	0.28

Triangulated primal graph

Density: 67.43%
MCB compute time (ms): 10,621
MCB cycles: 9,118
Triangles: None

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

Clustering coefficient 0.81 1.00 0.88 0.87 137.10 0.00 -20.45 0.06 0.06 2.56

Degree 23 135 104.51 116.50 16,304 MAX VALUE 710.23 34.86 0.33 2.44

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 27,354 MAX VALUE 10,017.10 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.81	1.00	0.88	0.87	137.10	0.00	-20.45	0.06	0.06	2.56
Degree	23	135	104.51	116.50	16,304	MAX VALUE	710.23	34.86	0.33	2.44
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	27,354	MAX VALUE	10,017.10	0.00	0.00	0.00

Dual graph

Density: 52.00%
MCB compute time (ms): 1
MCB cycles: 132
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/Dual1.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 12 13 12.48 12.00 312 2.49e+27 63.08 0.50 0.04 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 528 MAX VALUE 182.99 0.00 0.00 0.00

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	12	13	12.48	12.00	312	2.49e+27	63.08	0.50	0.04	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	528	MAX VALUE	182.99	0.00	0.00	0.00

Minimal dual graph

Density: 52.00%
MCB compute time (ms): 1
MCB cycles: 132

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 12 13 12.48 12.00 312 2.49e+27 63.08 0.50 0.04 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 528 MAX VALUE 182.99 0.00 0.00 0.00

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	12	13	12.48	12.00	312	2.49e+27	63.08	0.50	0.04	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	528	MAX VALUE	182.99	0.00	0.00	0.00

Triangulated dual graph

Density: 74.00%
Triangles: 1,078

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

Clustering coefficient 0.72 1.00 0.86 1.00 21.61 0.02 -3.99 0.14 0.16 0.69

Degree 12 24 17.76 12.00 444 3.91e+30 70.44 6.00 0.34 0.69

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	0.72	1.00	0.86	1.00	21.61	0.02	-3.99	0.14	0.16	0.69
Degree	12	24	17.76	12.00	444	3.91e+30	70.44	6.00	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 74.00%

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

Clustering coefficient 0.72 1.00 0.86 1.00 21.61 0.02 -3.99 0.14 0.16 0.69

Degree 12 24 17.76 12.00 444 3.91e+30 70.44 6.00 0.34 0.69

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	0.72	1.00	0.86	1.00	21.61	0.02	-3.99	0.14	0.16	0.69
Degree	12	24	17.76	12.00	444	3.91e+30	70.44	6.00	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.92%
MCB compute time (ms): 38
MCB cycles: 132
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-13-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 13 3.45 2.00 624 MAX VALUE 171.21 3.62 1.05 0.50

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,056 MAX VALUE 274.49 0.00 0.00 0.00

XCSP 2.1 Benchmarks