  We introduce a new geometric spanner, $\delta$-Greedy, whose construction is
based on a generalization of the known Path-Greedy and Gap-Greedy spanners. The
$\delta$-Greedy spanner combines the most desirable properties of geometric
spanners both in theory and in practice. More specifically, it has the same
theoretical and practical properties as the Path-Greedy spanner: a natural
definition, small degree, linear number of edges, low weight, and strong
$(1+\varepsilon)$-spanner for every $\varepsilon>0$. The $\delta$-Greedy
algorithm is an improvement over the Path-Greedy algorithm with respect to the
number of shortest path queries and hence with respect to its construction
time. We show how to construct such a spanner for a set of $n$ points in the
plane in $O(n^2 \log n)$ time.
  The $\delta$-Greedy spanner has an additional parameter, $\delta$, which
indicates how close it is to the Path-Greedy spanner on the account of the
number of shortest path queries. For $\delta = t$ the output spanner is
identical to the Path-Greedy spanner, while the number of shortest path queries
is, in practice, linear.
  Finally, we show that for a set of $n$ points placed independently at random
in a unit square the expected construction time of the $\delta$-Greedy
algorithm is $O(n \log n)$. Our analysis indicates that the $\delta$-Greedy
spanner gives the best results among the known spanners of expected $O(n \log
n)$ time for random point sets. Moreover, the analysis implies that by setting
$\delta = t$, the $\delta$-Greedy algorithm provides a spanner identical to the
Path-Greedy spanner in expected $O(n \log n)$ time.
