(A) push-insert lower bounding method for the frequency assignment problem

Abstract

The frequency assignment problem belongs to the class of NP-complete. Therefore it is necessary to use more time efficient algorithms which cannot guarantee optimal solution. Thus, if we can find more time efficient method to obtain a lower bound which is closer to the optimum, a lower bound obtained by this method can be a good information on how far away a feasible solution is from the optimum and on what heuristic approach is effective for a frequency assignment problem with specific structure. The objective of this thesis is to suggest a new lower bounding method for the frequency assignment problem by using frequency-insert concepts such as natural insert and push-insert. In natural insert scheme, requirements can be assigned to the unused frequencies without increasing the span. However, push-insert can assigns the unused frequencies to requirements only with increasing the current span. A lower bound is obtained by solving simple maximnal flow problems to find out upper bounds on the number of frequency-inserts and natural inserts. Compared with some of lower bounds suggested by Gamst, the new lower bound obtained by this method is proved to be closer to the optimum. And it can be seen easily that this method is more time efficient.