  We use a set of four theoretical navigability indices for street maps to
investigate the shape of the resulting street networks, if they are grown by
optimizing these indices. The indices compare the performance of simulated
navigators (having a partial information about the surroundings, like humans in
many real situations) to the performance of optimally navigating individuals.
We show that our simple greedy shortcut construction strategy generates the
emerging structures that are different from real road network, but not
inconceivable. The resulting city plans, for all navigation indices, share
common qualitative properties such as the tendency for triangular blocks to
appear, while the more quantitative features, such as degree distributions and
clustering, are characteristically different depending on the type of metrics
and routing strategies. We show that it is the type of metrics used which
determines the overall shapes characterized by structural heterogeneity, but
the routing schemes contribute to more subtle details of locality, which is
more emphasized in case of unrestricted connections when the edge crossing is
allowed.
