Dynamic algorithms for classes of constraint satisfaction problems

Daniele Frigioni, Alberto Marchetti-Spaccamela, Umberto Nanni

Abstract: Many fundamental tasks in artificial intelligence and in combinatorial optimization can be formulated as a Constraint Satisfaction Problem (CSP). It is the problem of finding an assignment of values for a set of variables, each defined on a finite domain of feasible values, subject to a given collection of constraints. Each constraint is defined over a set of variables and specifies the allowed combinations of values as a collection of tuples. In general, the problem of finding a solution to a CSP is NP-complete, but in some cases it has shown to be polynomially solvable. We consider the dynamic version of some polynomially solvable constraint satisfaction problems, and present solutions that are better than recomputing everything from scratch after each update. The updates we consider are either restrictions, i.e., deletions of values from existing constraints and introduction of new constraints, or relaxations, i.e., insertions of values or deletions of constraints.