Routing Among Convex Polygonal Obstacles in the Plane

Given a set [Formula: see text] of [Formula: see text] pairwise disjoint convex polygonal obstacles in the plane, defined with [Formula: see text] vertices, we preprocess [Formula: see text] and compute one routing table at each vertex in a subset of vertices of [Formula: see text]. For routing a packet from any vertex [Formula: see text] to any vertex [Formula: see text], our scheme computes a routing path with a multiplicative stretch [Formula: see text] and an additive stretch [Formula: see text], by consulting routing tables at only a subset of vertices along that path. Here, [Formula: see text] is the number of obstacles of [Formula: see text] the routing path intersects, and [Formula: see text] depends on the geometry of obstacles in [Formula: see text]. During the preprocessing phase, we construct routing tables of size [Formula: see text] in [Formula: see text] time, where [Formula: see text] is an input parameter.