  Suppose that we are given two independent sets $I_b$ and $I_r$ of a graph
such that $|I_b|=|I_r|$, and imagine that a token is placed on each vertex in
$I_b$. Then, the sliding token problem is to determine whether there exists a
sequence of independent sets which transforms $I_b$ into $I_r$ so that each
independent set in the sequence results from the previous one by sliding
exactly one token along an edge in the graph. This problem is known to be
PSPACE-complete even for planar graphs, and also for bounded treewidth graphs.
In this paper, we thus study the problem restricted to trees, and give the
following three results: (1) the decision problem is solvable in linear time;
(2) for a yes-instance, we can find in quadratic time an actual sequence of
independent sets between $I_b$ and $I_r$ whose length (i.e., the number of
token-slides) is quadratic; and (3) there exists an infinite family of
instances on paths for which any sequence requires quadratic length.
