XCSP 2.1 Benchmark Database

Instance: normalized-ii-8a2-ext
Number of variables: 360
Number of constraints: 974
Satisfiable: True
Timestamp: 2025-07-27 21:34:21
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 360
Number of constraints: 974

General features

Coarse blocks: 17,544
Value tables: 618

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

Arity 2 8 2.43 2.00 2,364 MAX VALUE 773.68 1.51 0.62 0.31

Coarse blocks size 1 128 15.09 4.00 264,672 MAX VALUE 32,710.90 28.56 1.89 1.98

Relational linkage 0.50 1.00 0.96 1.00 6,829.59 0.00 -405.04 0.13 0.14 0.59

Tightness 0.00 0.25 0.23 0.25 225.45 0.00 -1,638.60 0.06 0.28 0.31

Tuples 3 255 19.39 3.00 18,882 MAX VALUE 1,379.23 60.79 3.14 0.31

Values 2 2 2.00 2.00 720 MAX VALUE 249.53 0.00 0.00 0.00

Value table constraints 2 14 4.66 2.00 2,880 MAX VALUE 796.29 3.34 0.72 1.62

Value table partitions 2 64 11.53 2.00 7,128 MAX VALUE 998.13 16.91 1.47 1.31

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	8	2.43	2.00	2,364	MAX VALUE	773.68	1.51	0.62	0.31
Coarse blocks size	1	128	15.09	4.00	264,672	MAX VALUE	32,710.90	28.56	1.89	1.98
Relational linkage	0.50	1.00	0.96	1.00	6,829.59	0.00	-405.04	0.13	0.14	0.59
Tightness	0.00	0.25	0.23	0.25	225.45	0.00	-1,638.60	0.06	0.28	0.31
Tuples	3	255	19.39	3.00	18,882	MAX VALUE	1,379.23	60.79	3.14	0.31
Values	2	2	2.00	2.00	720	MAX VALUE	249.53	0.00	0.00	0.00
Value table constraints	2	14	4.66	2.00	2,880	MAX VALUE	796.29	3.34	0.72	1.62
Value table partitions	2	64	11.53	2.00	7,128	MAX VALUE	998.13	16.91	1.47	1.31

Tree decomposition

Number of clusters: 252
Number of leaves: 46
Tree depth: 25
CIR: 0.80
Independent Cluster Pairs: 25,069
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/Tree1.json

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

Cluster constraints 0 72 15.12 3.00 3,810 0 None 23.95 1.58 2.64

Variables per cluster 5 52 14.36 16.00 3,619 MAX VALUE 637.31 7.46 0.52 2.00

Separator constraints 0 64 11.25 0.00 2,836 0 None 21.06 1.87 1.77

Separator variables 0 42 12.93 15.00 3,259 0 None 6.75 0.52 2.07

Clusters per var 1 29 10.05 9.00 3,619 MAX VALUE 697.17 6.92 0.69 3.06

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	72	15.12	3.00	3,810	0	None	23.95	1.58	2.64
Variables per cluster	5	52	14.36	16.00	3,619	MAX VALUE	637.31	7.46	0.52	2.00
Separator constraints	0	64	11.25	0.00	2,836	0	None	21.06	1.87	1.77
Separator variables	0	42	12.93	15.00	3,259	0	None	6.75	0.52	2.07
Clusters per var	1	29	10.05	9.00	3,619	MAX VALUE	697.17	6.92	0.69	3.06

Dual tree decomposition

Number of clusters: 354
Number of leaves: 180
Tree depth: 9
CIR: 0.78
Independent Cluster Pairs: 48,623
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/DualTree1.json

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

Cluster constraints 24 307 79.82 59.00 28,258 MAX VALUE 1,479.35 58.83 0.74 3.33

Variables per cluster 9 85 23.03 17.00 8,154 MAX VALUE 1,039.17 17.04 0.74 3.10

Separator constraints 0 184 58.27 43.00 20,626 0 None 40.08 0.69 3.29

Separator variables 0 63 20.28 16.00 7,180 0 None 13.79 0.68 3.06

Clusters per variable 1 42 8.37 8.00 8,154 MAX VALUE 1,701.63 6.97 0.83 2.43

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	24	307	79.82	59.00	28,258	MAX VALUE	1,479.35	58.83	0.74	3.33
Variables per cluster	9	85	23.03	17.00	8,154	MAX VALUE	1,039.17	17.04	0.74	3.10
Separator constraints	0	184	58.27	43.00	20,626	0	None	40.08	0.69	3.29
Separator variables	0	63	20.28	16.00	7,180	0	None	13.79	0.68	3.06
Clusters per variable	1	42	8.37	8.00	8,154	MAX VALUE	1,701.63	6.97	0.83	2.43

Primal graph

Density: 2.70%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/Primal1.json

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

Clustering coefficient 0.00 0.76 0.36 0.33 128.31 0.00 None 0.36 1.00 1.50

Degree 4 15 9.70 9.00 3,492 MAX VALUE 796.40 3.31 0.34 2.04

Eccentricity 5 8 6.57 7.00 2,364 MAX VALUE 672.13 1.12 0.17 1.38

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	0.00	0.76	0.36	0.33	128.31	0.00	None	0.36	1.00	1.50
Degree	4	15	9.70	9.00	3,492	MAX VALUE	796.40	3.31	0.34	2.04
Eccentricity	5	8	6.57	7.00	2,364	MAX VALUE	672.13	1.12	0.17	1.38
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 9.27%
MCB compute time (ms): None
MCB cycles: None
Triangles: None

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

Clustering coefficient 0.47 1.00 0.79 0.78 283.19 0.00 -92.45 0.14 0.18 4.31

Degree 4 96 33.29 28.00 11,984 MAX VALUE 1,138.38 26.57 0.80 3.77

Eccentricity 3 5 3.92 4.00 1,411 MAX VALUE 486.85 0.64 0.16 0.96

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	0.47	1.00	0.79	0.78	283.19	0.00	-92.45	0.14	0.18	4.31
Degree	4	96	33.29	28.00	11,984	MAX VALUE	1,138.38	26.57	0.80	3.77
Eccentricity	3	5	3.92	4.00	1,411	MAX VALUE	486.85	0.64	0.16	0.96
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 1.61%
MCB compute time (ms): 54,927
MCB cycles: 7,685
Triangles: 19,470
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/Dual1.json

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

Clustering coefficient 0.00 0.78 0.51 0.49 494.34 0.00 None 0.11 0.21 2.77

Degree 6 21 15.67 17.00 15,264 MAX VALUE 2,651.35 3.45 0.22 2.34

Eccentricity 5 8 6.17 6.00 6,010 MAX VALUE 1,766.76 0.68 0.11 0.94

MCB cycle size 3 10 3.33 3.00 25,586 MAX VALUE 9,091.60 0.83 0.25 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.78	0.51	0.49	494.34	0.00	None	0.11	0.21	2.77
Degree	6	21	15.67	17.00	15,264	MAX VALUE	2,651.35	3.45	0.22	2.34
Eccentricity	5	8	6.17	6.00	6,010	MAX VALUE	1,766.76	0.68	0.11	0.94
MCB cycle size	3	10	3.33	3.00	25,586	MAX VALUE	9,091.60	0.83	0.25	0.69

Minimal dual graph

Density: 0.38%
MCB compute time (ms): 9,932
MCB cycles: 815

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

Clustering coefficient 0.00 0.62 0.02 0.00 22.36 0.00 None 0.10 4.25 0.36

Degree 2 8 3.67 3.00 3,576 MAX VALUE 1,232.93 1.09 0.30 1.07

Eccentricity 8 12 10.60 11.00 10,328 MAX VALUE 2,295.69 0.96 0.09 1.35

MCB cycle size 3 12 6.55 7.00 5,340 MAX VALUE 1,484.56 2.04 0.31 1.97

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.62	0.02	0.00	22.36	0.00	None	0.10	4.25	0.36
Degree	2	8	3.67	3.00	3,576	MAX VALUE	1,232.93	1.09	0.30	1.07
Eccentricity	8	12	10.60	11.00	10,328	MAX VALUE	2,295.69	0.96	0.09	1.35
MCB cycle size	3	12	6.55	7.00	5,340	MAX VALUE	1,484.56	2.04	0.31	1.97

Triangulated dual graph

Density: 8.09%
Triangles: 983,207

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

Clustering coefficient 0.17 1.00 0.84 0.84 816.61 0.00 -188.98 0.13 0.15 4.65

Degree 8 562 78.69 83.00 76,646 MAX VALUE 3,894.45 66.44 0.84 3.84

Eccentricity 2 4 3.08 3.00 3,004 MAX VALUE 1,091.99 0.33 0.11 0.40

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.17	1.00	0.84	0.84	816.61	0.00	-188.98	0.13	0.15	4.65
Degree	8	562	78.69	83.00	76,646	MAX VALUE	3,894.45	66.44	0.84	3.84
Eccentricity	2	4	3.08	3.00	3,004	MAX VALUE	1,091.99	0.33	0.11	0.40

Triangulated minimal dual graph

Density: 2.38%

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

Clustering coefficient 0.18 1.00 0.79 0.72 765.15 0.00 -263.02 0.18 0.23 3.44

Degree 2 265 23.11 7.00 22,510 MAX VALUE 2,314.52 31.53 1.36 3.29

Eccentricity 3 6 4.58 5.00 4,462 MAX VALUE 1,475.60 0.53 0.12 0.77

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.18	1.00	0.79	0.72	765.15	0.00	-263.02	0.18	0.23	3.44
Degree	2	265	23.11	7.00	22,510	MAX VALUE	2,314.52	31.53	1.36	3.29
Eccentricity	3	6	4.58	5.00	4,462	MAX VALUE	1,475.60	0.53	0.12	0.77

Incidence graph

Density: 0.27%
MCB compute time (ms): 12,699
MCB cycles: 1,031
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8a2-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 14 3.54 2.00 4,728 MAX VALUE 1,391.14 2.80 0.79 1.11

Eccentricity 10 16 13.19 13.00 17,600 MAX VALUE 3,431.98 1.54 0.12 1.57

MCB cycle size 4 20 7.74 8.00 7,984 MAX VALUE 2,005.52 3.83 0.49 1.16

XCSP 2.1 Benchmarks