Routing Among Convex Polygonal Obstacles in the Plane

Given a set P of h pairwise disjoint convex polygonal obstacles in the plane, defined with n vertices, we preprocess P and compute one routing table at each vertex in a subset of vertices of P. For routing a packet from any vertex s is an element of P to any vertex t is an element of P, our scheme computes a routing path with a multiplicative stretch 1 + epsilon and an additive stretch 2kl, by consulting routing tables at only a subset of vertices along that path. Here, k is the number of obstacles of P the routing path intersects, and l depends on the geometry of obstacles in P. During the preprocessing phase, we construct routing tables of size O(n + h(3)/epsilon(2) polylog(h/epsilon)) in O(n + h(3)/epsilon(2) polylog(h/epsilon)) time, where epsilon < 1 is an input parameter.