An algorithm for Steiner trees in grid graphs and its application to homotopic routing

In this paper we present an algorithm for Steiner minimal trees in grid graphs with all terminals located on the boundary of the graph. The algorithm runs in O(min{k(4), k(2)n}) time, where k and n are the numbers of terminals and vertices of the graph, respectively. It can handle non-convex boundaries and is the fastest known for this case. We also consider the homotopic routing problem and apply our Steiner tree algorithm to construct minimum-length mires for multi-terminal nets.