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What is map colouring as a constraint problem?

  • A.Regions are variables, colours are the domain and neighbours must differ
  • B.Colours are variables and regions are the values assigned to them
  • C.Borders are variables and their lengths are constrained
  • D.The map is a single variable whose domain is all colourings

Answer: A

The standard formulation makes each region a variable whose domain is the available colours, with a binary inequality constraint between every pair of adjacent regions. It is the textbook example because the constraint graph is the map's adjacency graph and can be drawn. The alternatives invert the roles or collapse the structure. Choosing what to make a variable is the first modelling decision and it determines everything that follows.

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