Routing in Polygons with Holes

Sending a message through an unknown network is a difficult problem. In this paper, we consider the case in which, during a preprocessing phase, we assign a label and a routing table to each node. The routing strategy must then decide where to send the package using only the label of the target node and the routing table of the node the message is currently at. In this paper, we present the first routing scheme for the particular case in which the network is defined by the visibility graph of a polygon with n vertices and h holes. For any ε > 0 the routing scheme provides stretch at most 1 + ε. The labels have O(log n) bits and the corresponding routing tables are of size O(ε−1(h + 1) log n). The preprocessing time is O(n2 log n+ (h+ 1)n + ε−1(h+ 1)n) and can be improved to O(n2 + ε−1n) for simple polygons.