The Nielsen number on aspherical figure-eight type polyhedra

Let X be a compact polyhedron that is homotopy equivalent to the figure-eight. This is a survey paper for the WYK algorithm which provides computations for the Nielsen number of self-maps of X. The WYK algorithm consists of three parts and each part was introduced separately by Wagner [11], Yi and Kim [12], and Kim [8]. In this paper, we present the whole algorithm so that people can more easily use the algorithm.