Partially persistent dynamic sets for history-sensitive heuristics

EEectiveheuristic algorithmsfor combinatorialproblemsare based on integrating local neighborhood search with history-sensitive schemes, where the information collected during the previous search phase is used to direct the future eeort. In particular, some algorithms (like Strict Tabu Search and Reactive Tabu Search) need to detect whether a connguration has already been encountered during the previous phase of the search, either to prohibit repetitions or to determine a prohibition parameter in an adaptive way. This paper analyzes the use of persistent dynamic sets for storing and retrieving states and discusses the advantages of this option with respect to popular but less eecient realizations. If the search space is given by L-bit binary strings, the method complexity is O(L) average-case time per search iteration when hashing is used, while the total space for a sequence of t iterations is O(t). A concrete realization of the abstract data type through a C++ class is presented. The obtained memory occupation and timing results are analyzed for selected \dictionary" benchmark tasks and for the use of the structure to support history{sensitive heuristic algorithms, in particular for the Maximum Clique problem in graphs.