Chapter 9 - Solution synthesis

Abstract

Solution synthesis techniques constructively generate legal compound labels rather than eliminating redundant labels or redundant compound labels. One can see solution synthesis as a special case of problem reduction in which the n-constraint for a problem with n variables is constructed, and all the n-compound labels that violate some constraints are removed. Alternatively, solution synthesis can be seen as searching multiple partial compound labels in parallel. This chapter introduces three solution synthesis algorithms, namely, Freuder's algorithm, Seidel's invasion algorithm, and a class of algorithms called the Essex Algorithms. The idea of solution synthesis in the constraint satisfaction problems (CSPs) was first introduced by Freuder. Freuder's algorithm is applicable to general CSPs in which one wants to find all the solutions. The invasion algorithm is used to find all solutions for binary CSPs. It is possible to extend it to handle general CSPs; however, using it for solving CSPs that have k-ary constraints for large k would be inefficient. The invasion algorithm exploits the topology of the constraint graph and is especially useful for problems in which every variable is involved in only a few constraints.