XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-words-vg12-16-ext
Number of variables: 192
Number of constraints: 28
Satisfiable: True
Timestamp: 2025-07-20 22:09:45
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 192
Number of constraints: 28

General features

Coarse blocks: 7,648
Value tables: 192

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

Arity 12 16 13.71 12.00 384 5.20e+31 73.03 1.98 0.14 0.68

Coarse blocks size 1 624 49.81 13.00 380,928 MAX VALUE 20,484.10 78.78 1.58 4.21

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -141,793.00 0.00 0.95 2.70

Tightness 1.00 1.00 1.00 1.00 28.00 1.00 -0.00 0.00 0.00 0.68

Tuples 103 1,881 1,119.00 1,881.00 31,332 MAX VALUE 176.25 879.88 0.79 0.68

Values 26 26 26.00 26.00 4,992 MAX VALUE 625.55 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 384 MAX VALUE 133.08 0.00 0.00 0.00

Value table partitions 17 26 24.27 25.00 4,660 MAX VALUE 611.80 1.75 0.07 1.72

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	12	16	13.71	12.00	384	5.20e+31	73.03	1.98	0.14	0.68
Coarse blocks size	1	624	49.81	13.00	380,928	MAX VALUE	20,484.10	78.78	1.58	4.21
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-141,793.00	0.00	0.95	2.70
Tightness	1.00	1.00	1.00	1.00	28.00	1.00	-0.00	0.00	0.00	0.68
Tuples	103	1,881	1,119.00	1,881.00	31,332	MAX VALUE	176.25	879.88	0.79	0.68
Values	26	26	26.00	26.00	4,992	MAX VALUE	625.55	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	384	MAX VALUE	133.08	0.00	0.00	0.00
Value table partitions	17	26	24.27	25.00	4,660	MAX VALUE	611.80	1.75	0.07	1.72

Tree decomposition

Number of clusters: 26
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-vg12-16-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-ext/Tree1.json

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

Cluster constraints 0 2 1.08 1.00 28 0 None 0.92 0.85 1.01

Variables per cluster 27 120 47.08 37.00 1,224 MAX VALUE 96.61 27.83 0.59 1.52

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

Separator variables 0 96 39.69 31.00 1,032 0 None 21.27 0.54 1.58

Clusters per var 1 8 6.38 7.00 1,224 MAX VALUE 336.65 2.03 0.32 1.64

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.08	1.00	28	0	None	0.92	0.85	1.01
Variables per cluster	27	120	47.08	37.00	1,224	MAX VALUE	96.61	27.83	0.59	1.52
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	96	39.69	31.00	1,032	0	None	21.27	0.54	1.58
Clusters per var	1	8	6.38	7.00	1,224	MAX VALUE	336.65	2.03	0.32	1.64

Dual tree decomposition

Number of clusters: 16
Number of leaves: 2
Tree depth: 8
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-ext/DualTree1.json

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

Cluster constraints 12 12 12.00 12.00 192 1.85e+17 39.76 0.00 0.00 0.00

Variables per cluster 13 13 13.00 13.00 208 6.65e+17 41.04 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 11.25 12.00 180 0 None 2.90 0.26 0.23

Clusters per variable 1 16 7.43 1.00 208 2.81e+14 33.27 7.42 1.00 0.68

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	12	12	12.00	12.00	192	1.85e+17	39.76	0.00	0.00	0.00
Variables per cluster	13	13	13.00	13.00	208	6.65e+17	41.04	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	11.25	12.00	180	0	None	2.90	0.26	0.23
Clusters per variable	1	16	7.43	1.00	208	2.81e+14	33.27	7.42	1.00	0.68

Primal graph

Density: 13.61%
MCB compute time (ms): 1,046
MCB cycles: 2,305
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-ext/Primal1.json

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

Clustering coefficient 0.49 0.49 0.49 0.49 94.52 0.00 -136.06 0.00 0.00 0.00

Degree 26 26 26.00 26.00 4,992 MAX VALUE 625.55 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.07 3.00 7,080 MAX VALUE 2,579.77 0.26 0.08 0.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.49	0.49	0.49	94.52	0.00	-136.06	0.00	0.00	0.00
Degree	26	26	26.00	26.00	4,992	MAX VALUE	625.55	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.07	3.00	7,080	MAX VALUE	2,579.77	0.26	0.08	0.26

Triangulated primal graph

Density: 67.76%
MCB compute time (ms): 8,833
MCB cycles: 15,741
Triangles: None

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

Clustering coefficient 0.82 1.00 0.88 0.87 169.23 0.00 -24.57 0.05 0.06 2.33

Degree 26 165 129.42 145.00 24,848 MAX VALUE 914.79 43.13 0.33 2.33

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 47,223 MAX VALUE 17,293.30 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.82	1.00	0.88	0.87	169.23	0.00	-24.57	0.05	0.06	2.33
Degree	26	165	129.42	145.00	24,848	MAX VALUE	914.79	43.13	0.33	2.33
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	47,223	MAX VALUE	17,293.30	0.00	0.00	0.00

Dual graph

Density: 50.79%
MCB compute time (ms): 1
MCB cycles: 165
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-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 16 13.71 12.00 384 5.20e+31 73.03 1.98 0.14 0.68

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 660 MAX VALUE 228.74 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	16	13.71	12.00	384	5.20e+31	73.03	1.98	0.14	0.68
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	660	MAX VALUE	228.74	0.00	0.00	0.00

Minimal dual graph

Density: 50.79%
MCB compute time (ms): 1
MCB cycles: 165

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 16 13.71 12.00 384 5.20e+31 73.03 1.98 0.14 0.68

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 660 MAX VALUE 228.74 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	16	13.71	12.00	384	5.20e+31	73.03	1.98	0.14	0.68
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	660	MAX VALUE	228.74	0.00	0.00	0.00

Triangulated dual graph

Density: 68.25%
Triangles: 1,276

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

Clustering coefficient 0.66 1.00 0.85 1.00 23.90 0.01 -5.02 0.17 0.20 0.68

Degree 12 27 18.43 12.00 516 2.78e+34 79.31 7.42 0.40 0.68

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	0.66	1.00	0.85	1.00	23.90	0.01	-5.02	0.17	0.20	0.68
Degree	12	27	18.43	12.00	516	2.78e+34	79.31	7.42	0.40	0.68
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 68.25%

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

Clustering coefficient 0.66 1.00 0.85 1.00 23.90 0.01 -5.02 0.17 0.20 0.68

Degree 12 27 18.43 12.00 516 2.78e+34 79.31 7.42 0.40 0.68

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	0.66	1.00	0.85	1.00	23.90	0.01	-5.02	0.17	0.20	0.68
Degree	12	27	18.43	12.00	516	2.78e+34	79.31	7.42	0.40	0.68
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.59%
MCB compute time (ms): 56
MCB cycles: 165
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg12-16-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 16 3.49 2.00 768 MAX VALUE 206.11 3.97 1.14 0.47

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,320 MAX VALUE 343.11 0.00 0.00 0.00

XCSP 2.1 Benchmarks