Easy to be Hard: Difficult Problems for Greedy Algorithms

Abstract

Recent advances in hill-climbing satisfiability methods have solved hard classes of problems, which are difficult for existing systematic methods such as Davis-Putnam. In this paper we examine a class of problems derived from crossword puzzles that is difficult for the hill-climbing methods, yet is easily solved by standard forward-checking algorithms. The characteristic feature of this class is its hierarchical nature: clusters of dependent variables, with a small number of connections between the clusters. Although the results are experimental and not theoretical, we speculate that any hierarchical constraint-satisfaction problem with certain characteristics will be difficult for naive greedy algorithms.