Frequency assignment algorithms have relation with the use of a recently developed technique based on the theory of graph coloring. Numerous algorithms exist for frequency assignment problems, it should be capable of accommodating as many users as possible with the limited frequency resource available. We introduce a new algorithm for frequency assignment problem. First, we define the difficulty measure of nodes that is based on new definition of node subsets. Next, we attempt to classify four essential assignment methods. By using the defined difficulty measure and assignment methods, we construct a new algorithm which include a new assignment concept, so called pushinsert. In addition, we show that the algorithm is very useful in solving for the frequency assignment problem.