Distance-Preserving Approximations of Polygonal Paths

Given a polygonal path P with vertices p1, p2, . . . , pn ∈ Rd and a real number t ≥ 1, a path Q = (pi1 , pi2 , . . . , pik) is a t-distance-preserving approximation of P if 1 = i1 < i2 < . . . < ik = n and each straight-line edge (pij , pij+1) of Q approximates the distance between pij and pij+1 along the path P within a factor of t. We present exact and approximation algorithms that compute such a path Q that minimizes k (when given t) or t (when given k). We also present some experimental results.