Introduction to the Maximum SolutionProblem

This paper surveys complexity and approximability results for the Maximum Solution (Max Sol) problem. Max Sol is an optimisation variant of the constraint satisfaction problem. Many important and well-known combinatorial optimisation problems are instances of Max Sol: for example, Max Sol restricted to the domain {0, 1} is exactly the Max Ones problem (which, in turn, captures problems such as Independent Set and 0/1 Integer Programming). By using this relationship, many different problems in logic, graph theory, integer programming, and algebra can be given a uniform treatment. This opens up for new ways of analysing and solving combinatorial optimisation problems.