A large number of problems in AI and other areas of computer science can be viewed as special cases of the constraint-satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, the planning of genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions.

The traditional approach for solving Constraint satisfaction Problems (CSPs) is searching the Assignment Space in which each state represents an assignment to some variables. This paper suggests a new search space formalization for CSPs, the Partial Domain Search Tree (PDST). In each PDST node aunique subset of the original domain is considered, values are excluded from the domains in each node to insure that a given set of constraints is satisfied. We provide theoretical analysis of this new approach showing that searching the PDST is beneficial for loosely constrained problems. Experimental results show that this new formalization is a promising direction for future research. In some cases searching the PDST outperforms the traditional approach by an order of magnitude. Furthermore, PDST can enhance Local Search techniques resulting in solutions that violate up to 30% less constraints.

CSP solvers usually search a partial assignment search tree.We present a new formalization for CSP solvers, which spansa conceptually different search tree, where each node representssubsets of the original domains for the variables. We experimentwith a simple backtracking algorithm for this searchtree and show that it outperforms a simple backtracking algorithmon the traditional search tree in many cases.

A large number of problems in AI and other areas of computer science can be viewed as special cases of the constraint-satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, the planning of genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem.

A large number of problems in AI and other areas of computer science can be viewed as special cases of the constraint-satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, the planning of genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques.

Many AI tasks can be formulated as constraint-satisfaction problems (CSP), i.e., the assignment of values to variables subject to a set of constraints. While some CSPs are hard, those that are easy can often be mapped into sparse networks of constraints which, in the extreme case, are trees. This paper identifies classes of problems that lend themselves to easy solutions, and develops algorithms that solve these problems optimally. The paper then presents a method of generating heuristic advice to guide the order of value assignments based on both the sparseness found in the constraint network and the simplicity of tree-structured CSPs. The advice is generated by simplifying the pending subproblems into trees, counting the number of consistent solutions in each simplified subproblem, and comparing these counts to decide among the choices pending in the original problem.