Guillaume studies ‘constraint satisfaction problems’. Can constraints within a given set of variables all be fulfilled? The field has many applications, from logic games like Sudoku to the scheduling of sport leagues. Some constraint problems can be very hard, requiring the use of expertly-built solver programs. Guillaume looks at particularly difficult constraint satisfaction problems,  to identify what they have in common. His work seeks to find a widely applicable approach to  hard constraint problems in general. His team has developed a measure that evaluates the occurrence of a specific behavior (called completability) of constraint satisfaction problems and has  shown that the lower the completability, the harder the problem. They believe that their measure will improve the general understanding of constraint satisfaction and in time lead to even more efficients ways of solving such problems.