Colouring, constraint satisfaction, and complexity

Constraint satisfaction problems have enjoyed much attention since the early seventies, and in the last decade have become also a focus of attention amongst theoreticians. Graph colourings are a special class of constraint satisfaction problems; they offer a microcosm of many of the considerations that occur in constraint satisfaction. From the point of view of theory, they are well known to exhibit a dichotomy of complexity - the k-colouring problem is polynomial time solvable when k 2, and NP-complete when k 3. Similar dichotomy has been proved for the class of graph homomorphism problems, which are intermediate problems between graph colouring and constraint satisfaction. However, for general constraint satisfaction problems, dichotomy has only been conjectured. Although the conjecture remains unproven to this day, it has been driving much of the theoretical research on constraint satisfaction problems, which combines methods of logic, universal algebra, analysis, and combinatori...

• Type: Journal
• Year: 2008
• Where: CSR
• Authors: Pavol Hell, Jaroslav Nesetril
• Keywords: Constraint Satisfaction, Constraint Satisfaction Problems, CSR 2008, General Constraint Satisfaction, Theoretical Computer Science