Routing Through a Generalized Switchbox

Michael Kaufmann, Kurt Mehlhorn

Abstract: We present an algorithm for the routing problem for two-terminal nets in generalized switchboxes. A generalized switchbox is any subset R of the planar rectangular grid with no non-trivial holes, i.e. every finite face has exactly four incident vertices. A net is a pair of nodes of non-maximal degree on the boundary of R. A solution is a set of edge-disjoint paths, one for each net. Our algorithm solves generalized switchbox routing problems in time O(n(log n)2) where n is the number of vertices of R, i.e. it either finds a solution or indicates that there is none.