Minimum strictly fundamental cycle bases of planar graphs are hard to find

In this paper, we consider the problem of finding a spanning tree in a graph that minimizes the sum over the lengths of the cycles induced by the chords of the tree. We show the NPNP-completeness of this problem for planar graphs. The proof will be by reduction of a planar version of the Exact Cover By 3-Sets Problem. Finding such a minimum strictly fundamental cycle basis has various practical applications, e.g. in designing optimal periodic timetables in public transport.