The consistent labeling problem: part I

In this first part of a two-part paper we introduce a general consistent labeling problem based on a unit constraint relation T containing N-tuples of units which constrain one another, and a compatibility relation R containing N-tuples of unit-label pairs specifying which N-tuples of units are compatible with which N-tuples of labels. We show that Latin square puzzles, finding N-ary relations, graph or auto-mata homomorphisms, graph colorings, as well as determining satisfiability of propositional logic statements and solving scene and edge labeling problems, are all special cases of the general consistent labeling problem. We then discuss the various approaches that researchers have used to speed up the tree search required to find consistent labelings. Each of these approaches uses a particular look-ahead operator to help eliminate backtracking in the tree search. Finally, we define the ¿KP two-parameter class of look-ahead operators which includes, as special cases, the operators other researchers have used.