This article deals with dynamical system neural networks which find fo
r given vertices simple paths joining the vertices with optimal (short
est) or near-optimal length. Such neural networks might have a role in
scheduling a machine which wires integrated circuits. We develop a mo
dified guilty net algorithm which is fully parallel in vertex placemen
t; thus there might be efficient, albeit not perfect, implementations
in parallel. During iterations of the algorithm all vertices of a math
ematical path move in two-dimensional space until vertex positions coi
ncide with given physical vertices.