Global Constraint Catalog

  • Home
  • Title
  • Preface
  • Bibliography
  • Index
  • Content
  • 1. Getting started
  • 2. Describing Global Constraints
  • 3. Description of the Catalogue
  • 4. Further Topics
  • 5. Global Constraint Catalogue
  • 6. Legend for the Description

3. Description of the Catalogue

  • 3.1. Which global constraints are included?
  • 3.2. Which global constraints are missing?
  • 3.3. Searching in the catalogue
    • 3.3.1. How to see if a global constraint is in the catalogue?
    • 3.3.2. How to search for all global constraints sharing the same structure
      • 3.3.2.1. Searching from a graph property perspective
      • 3.3.2.2. Searching from an automaton perspective
      • 3.3.2.3. Searching from a first order logic perspective
    • 3.3.3. Searching all places where a global constraint is referenced
    • 3.3.4. Searching the mapping with a constraint of a concrete system
  • 3.4. Figures of the catalogue
  • 3.5. Constraints argument patterns
    • 3.5.1. Constraints with 1 argument
    • 3.5.2. Constraints with 2 arguments
    • 3.5.3. Constraints with 3 arguments
    • 3.5.4. Constraints with 4 arguments
    • 3.5.5. Constraints with 5 arguments
    • 3.5.6. Constraints with 6 arguments
    • 3.5.7. Constraints with 8 arguments
    • 3.5.8. Constraints with 10 arguments
  • 3.6. Meta-keywords attached to the keywords
    • 3.6.1. Application area
    • 3.6.2. Characteristic of a constraint
    • 3.6.3. Combinatorial object
    • 3.6.4. Complexity
    • 3.6.5. Constraint network structure
    • 3.6.6. Constraint type
    • 3.6.7. Constraint arguments
    • 3.6.8. Filtering
    • 3.6.9. Final graph structure
    • 3.6.10. Geometry
    • 3.6.11. Heuristics
    • 3.6.12. Miscellaneous
    • 3.6.13. Modelling
    • 3.6.14. Modelling exercises
    • 3.6.15. Problems
    • 3.6.16. Puzzles
    • 3.6.17. Symmetry
  • 3.7. Keywords attached to the global constraints
    • 3.7.1. 3-dimensional-matching
    • 3.7.2. 3-SAT
    • 3.7.3. Abstract interpretation
    • 3.7.4. Acyclic
    • 3.7.5. Aggregate
    • 3.7.6. Air traffic management
    • 3.7.7. Alignment
    • 3.7.8. All different
    • 3.7.9. Alpha-acyclic constraint network(2)
    • 3.7.10. Alpha-acyclic constraint network(3)
    • 3.7.11. Apartition
    • 3.7.12. Arc-consistency
    • 3.7.13. Arithmetic constraint
    • 3.7.14. Array constraint
    • 3.7.15. Assigning and scheduling tasks that run in parallel
    • 3.7.16. Assignment
    • 3.7.17. Assignment dimension
    • 3.7.18. Assignment to the same set of values
    • 3.7.19. At least
    • 3.7.20. At most
    • 3.7.21. Automaton
    • 3.7.22. Automaton with array of counters
    • 3.7.23. Automaton with counters
    • 3.7.24. Automaton with same input symbol
    • 3.7.25. Automaton without counters
    • 3.7.26. Autoref
    • 3.7.27. Balanced assignment
    • 3.7.28. Balanced tree
    • 3.7.29. Berge-acyclic constraint network
    • 3.7.30. Binary constraint
    • 3.7.31. Bioinformatics
    • 3.7.32. Bipartite
    • 3.7.33. Bipartite matching
    • 3.7.34. Bipartite matching in convex bipartite graphs
    • 3.7.35. Boolean channel
    • 3.7.36. Boolean constraint
    • 3.7.37. Border
    • 3.7.38. Bound-consistency
    • 3.7.39. Business rules
    • 3.7.40. Centered cyclic(1) constraint network(1)
    • 3.7.41. Centered cyclic(2) constraint network(1)
    • 3.7.42. Centered cyclic(3) constraint network(1)
    • 3.7.43. Channel routing
    • 3.7.44. Channelling constraint
    • 3.7.45. Circuit
    • 3.7.46. Circular sliding cyclic(1) constraint network(2)
    • 3.7.47. Cluster
    • 3.7.48. Coloured
    • 3.7.49. Compulsory part
    • 3.7.50. Conditional constraint
    • 3.7.51. Configuration problem
    • 3.7.52. Connected component
    • 3.7.53. Consecutive loops are connected
    • 3.7.54. Consecutive values
    • 3.7.55. Constraint between two collections of variables
    • 3.7.56. Constraint between three collections of variables
    • 3.7.57. Constraint involving set variables
    • 3.7.58. Constraint on the intersection
    • 3.7.59. Constructive disjunction
    • 3.7.60. Contact
    • 3.7.61. Contractible
    • 3.7.62. Convex
    • 3.7.63. Convex bipartite graph
    • 3.7.64. Convex hull relaxation
    • 3.7.65. Conway packing problem
    • 3.7.66. Core
    • 3.7.67. Costas arrays
    • 3.7.68. Cost filtering constraint
    • 3.7.69. Cost matrix
    • 3.7.70. Counting constraint
    • 3.7.71. Cumulative longest hole problems
    • 3.7.72. Cycle
    • 3.7.73. Cyclic
    • 3.7.74. Data constraint
    • 3.7.75. Deadlock breaking
    • 3.7.76. Decomposition
    • 3.7.77. Decomposition-based violation measure
    • 3.7.78. Demand profile
    • 3.7.79. Degree of diversity of a set of solutions
    • 3.7.80. Derived collection
    • 3.7.81. DFS-bottleneck
    • 3.7.82. Difference
    • 3.7.83. Difference between pairs of variables
    • 3.7.84. Directed acyclic graph
    • 3.7.85. Disequality
    • 3.7.86. Disjunction
    • 3.7.87. Domain channel
    • 3.7.88. Domain definition
    • 3.7.89. Dominating queens
    • 3.7.90. Domination
    • 3.7.91. Dual model
    • 3.7.92. Duplicated variables
    • 3.7.93. Dynamic programming
    • 3.7.94. Empty intersection
    • 3.7.95. Entailment
    • 3.7.96. Equality
    • 3.7.97. Equality between multisets
    • 3.7.98. Equivalence
    • 3.7.99. Euler knight
    • 3.7.100. Excluded
    • 3.7.101. Extensible
    • 3.7.102. Extension
    • 3.7.103. Facilities location problem
    • 3.7.104. Floor planning problem
    • 3.7.105. Flow
    • 3.7.106. Frequency allocation problem
    • 3.7.107. Functional dependency
    • 3.7.108. Geometrical constraint
    • 3.7.109. Glue matrix
    • 3.7.110. Golomb ruler
    • 3.7.111. Graph colouring
    • 3.7.112. Graph constraint
    • 3.7.113. Graph partitioning constraint
    • 3.7.114. Guillotine cut
    • 3.7.115. Hall interval
    • 3.7.116. Hamiltonian
    • 3.7.117. Heuristics
    • 3.7.118. Heuristics and Berge-acyclic constraint network
    • 3.7.119. Heuristics and lexicographical ordering
    • 3.7.120. Heuristics for two-dimensional rectangle placement problems
      • 3.7.120.1. Dual strategy for rectangle placement problems with no slack
      • 3.7.120.2. Strategy that gradually creates a compulsory part
    • 3.7.121. Hungarian method for the assignment problem
    • 3.7.122. Hybrid-consistency
    • 3.7.123. Hypergraph
    • 3.7.124. Included
    • 3.7.125. Inclusion
    • 3.7.126. Incompatible pairs of values
    • 3.7.127. Indistinguishable values
    • 3.7.128. Interval
    • 3.7.129. Involution
    • 3.7.130. Joker value
    • 3.7.131. Klee's measure problem
    • 3.7.132. Labelling by increasing cost
    • 3.7.133. Latin square
    • 3.7.134. Lexicographic order
    • 3.7.135. Limited discrepancy search
    • 3.7.136. Linear programming
    • 3.7.137. Line segments intersection
    • 3.7.138. Logic
    • 3.7.139. Logigraphe
    • 3.7.140. Magic hexagon
    • 3.7.141. Magic series
    • 3.7.142. Magic square
    • 3.7.143. Matching
    • 3.7.144. Matrix
    • 3.7.145. Matrix model
    • 3.7.146. Matrix symmetry
    • 3.7.147. Maximum
    • 3.7.148. Maximum clique
    • 3.7.149. Maximum number of occurrences
    • 3.7.150. maxint
    • 3.7.151. Metro
    • 3.7.152. Minimum
    • 3.7.153. Minimum cost flow
    • 3.7.154. Minimum feedback vertex set
    • 3.7.155. Minimum hitting set cardinality
    • 3.7.156. Minimum number of occurrences
    • 3.7.157. Modulo
    • 3.7.158. Multi-site employee scheduling with calendar constraints
    • 3.7.159. Multiset
    • 3.7.160. Multiset ordering
    • 3.7.161. No cycle
    • 3.7.162. No loop
    • 3.7.163. n-Amazons
    • 3.7.164. n-queens
    • 3.7.165. Non-deterministic automaton
    • 3.7.166. Non-overlapping
    • 3.7.167. Number of changes
    • 3.7.168. Number of distinct equivalence classes
    • 3.7.169. Number of distinct values
    • 3.7.170. Obscure
    • 3.7.171. One succ
    • 3.7.172. Open automaton constraint
    • 3.7.173. Open constraint
    • 3.7.174. Order constraint
    • 3.7.175. Orthotope
    • 3.7.176. Overlapping alldifferent
    • 3.7.177. Pair
    • 3.7.178. Packing almost squares
    • 3.7.179. Pallet loading
    • 3.7.180. Partition
    • 3.7.181. Path
    • 3.7.182. Partridge
    • 3.7.183. Pattern sequencing
    • 3.7.184. Pentomino
    • 3.7.185. Periodic
    • 3.7.186. Permutation
    • 3.7.187. Permutation channel
    • 3.7.188. Phi-tree
    • 3.7.189. Phylogeny
    • 3.7.190. Pick-up delivery
    • 3.7.191. Planarity test
    • 3.7.192. Polygon
    • 3.7.193. Positioning constraint
    • 3.7.194. Predefined constraint
    • 3.7.195. Preferences
    • 3.7.196. Producer-consumer
    • 3.7.197. Product
    • 3.7.198. Program verification
    • 3.7.199. Proximity constraint
    • 3.7.200. Pure functional dependency
    • 3.7.201. Quadtree
    • 3.7.202. Range
    • 3.7.203. Rank
    • 3.7.204. RCC8
    • 3.7.205. Rectangle clique partition
    • 3.7.206. Regret based heuristics
    • 3.7.207. Regret based heuristics in matrix problems
    • 3.7.208. Reified automaton constraint
    • 3.7.209. Reified constraint
    • 3.7.210. Relation
    • 3.7.211. Relaxation
    • 3.7.212. Relaxation dimension
    • 3.7.213. Resource constraint
    • 3.7.214. Reverse of a constraint
    • 3.7.215. Run of a permutation
    • 3.7.216. SAT
    • 3.7.217. Scalar product
    • 3.7.218. Sequence
    • 3.7.219. Sequence dependent set-up
    • 3.7.220. Sequencing with release times and deadlines
    • 3.7.221. Set channel
    • 3.7.222. Set packing
    • 3.7.223. Shikaku
    • 3.7.224. Scheduling constraint
    • 3.7.225. Scheduling with machine choice, calendars and preemption
    • 3.7.226. Shared table
    • 3.7.227. Schur number
    • 3.7.228. SLAM problem
    • 3.7.229. Sliding cyclic(1) constraint network(1)
    • 3.7.230. Sliding cyclic(1) constraint network(2)
    • 3.7.231. Sliding cyclic(1) constraint network(3)
    • 3.7.232. Sliding cyclic(2) constraint network(2)
    • 3.7.233. Sliding sequence constraint
    • 3.7.234. Smallest square for packing consecutive dominoes
    • 3.7.235. Smallest rectangle area
    • 3.7.236. Smallest square for packing rectangles with distinct sizes
    • 3.7.237. Soft constraint
    • 3.7.238. Sort
    • 3.7.239. Sort based reformulation
    • 3.7.240. Sparse functional dependency
    • 3.7.241. Sparse table
    • 3.7.242. Sport timetabling
    • 3.7.243. Squared squares
    • 3.7.244. Statistics
    • 3.7.245. Strip packing
    • 3.7.246. Strong articulation point
    • 3.7.247. Strong bridge
    • 3.7.248. Strongly connected component
    • 3.7.249. Subset sum
    • 3.7.250. Sudoku
    • 3.7.251. Sum
    • 3.7.252. Sweep
    • 3.7.253. Symmetric
    • 3.7.254. Symmetry
    • 3.7.255. System of constraints
    • 3.7.256. Table
    • 3.7.257. Temporal constraint
    • 3.7.258. Ternary constraint
    • 3.7.259. Timetabling constraint
    • 3.7.260. Time window
    • 3.7.261. Touch
    • 3.7.262. Tree
    • 3.7.263. Tuple
    • 3.7.264. Two-dimensional orthogonal packing
    • 3.7.265. Unary constraint
    • 3.7.266. Undirected graph
    • 3.7.267. Value constraint
    • 3.7.268. Value partitioning constraint
    • 3.7.269. Value precedence
    • 3.7.270. Variable-based violation measure
    • 3.7.271. Variable indexing
    • 3.7.272. Variable subscript
    • 3.7.273. Vector
    • 3.7.274. Vpartition
    • 3.7.275. Weighted assignment
    • 3.7.276. Workload covering
    • 3.7.277. Zebra puzzle
    • 3.7.278. Zero-duration task
<< 3.7.40. Centered cyclic(1) constraint network(1)3.7.42. Centered cyclic(3) constraint network(1) >>

3.7.41. Centered cyclic(2) constraint network(1)

  • πšŽπš•πšŽπš–,

  • πšŽπš•πšŽπš–πšŽπš—πš,

  • πšŽπš•πšŽπš–πšŽπš—πš_πšπš›πšŽπšŠπšπšŽπš›πšŽπšš,

  • πšŽπš•πšŽπš–πšŽπš—πš_πš•πšŽπšœπšœπšŽπšš,

  • πšŽπš•πšŽπš–πšŽπš—πš_πšœπš™πšŠπš›πšœπšŽ,

  • πš’πš—_πšœπšŠπš–πšŽ_πš™πšŠπš›πšπš’πšπš’πš˜πš—,

  • πš–πš’πš—πš’πš–πšžπš–_πšπš›πšŽπšŠπšπšŽπš›_πšπš‘πšŠπš—,

  • 𝚜𝚝𝚊𝚐𝚎_πšŽπš•πšŽπš–πšŽπš—πš.

Figure 3.7.10. Hypergraph associated with a centered cyclic(2) constraint network(1)
ctrs/preface-150-tikz

A constraint network corresponding to the pattern depicted by FigureΒ 3.7.10. Circles depict variables, while arcs are represented by a set of variables. Grey circles correspond to optional variables.

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