We consider the orienteering problem : Given a set P of
n points in the plane, a starting point r in P, and a
length constraint B, one need to find a tour starting at
r that visits as many points of P as possible and of
length not exceeding B. We present a
(1-µ)-approximation algorithm for this problem that runs in
n^{O(1/µ)} time, and visits at least
(1-µ)k points of P, where k is the number of
points visited by the optimal solution. This is the first polynomial
time approximation scheme(PTAS) for this problem.