  A tree t-spanner of an unweighted graph G is a spanning tree T such that for
every two vertices their distance in T is at most t times their distance in G.
Given an unweighted graph G and a positive integer t as input, the tree
t-spanner problem is to compute a tree t-spanner of G if one exists. This
decision problem is known to be NP-complete even in the restricted class of
unweighted planar graphs. We present a linear-time reduction from tree
t-spanner in outerplanar graphs to the supply-demand tree partition problem.
Based on this reduction, we obtain a linear-time algorithm to solve tree
t-spanner in outerplanar graphs. Consequently, we show that the minimum value
of t for which an input outerplanar graph on n vertices has a tree t-spanner
can be found in O(n log n) time.
