Defining Modularity, Hierarchy, and Repetition

In order to benefit from the presence of modularity, hierarchy, or repetition in a problem, a necessary first step is to identify precise notions of these problem features. Modularity, hierarchy, and repetition have often been used as terms to characterize the operation of a search method. However, if these features are to improve the efficiency of a search method, then there must exist corresponding problem features that permit such improvements. A primary question to be asked therefore is how these or other problem features may be defined in such a way that their identification by a search method guarantees potential efficiency improvements. The aim of this contribution is to provide such definitions, and to discuss how algorithms may exploit the corresponding efficiency improvements.