Routing Through a Generalized Switchbox

We present an algorithm for the routing problem for two-tenninal nets in generalized switchboxes. A generalized s\~itchbox 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 standard generalized switchbox routing problems in time 0(n(109 n)2) where n is the number of vertices of R, i.e. it either finds a solution or indicates that there is none. A problem is standard if deg(v) + ter(v) is even for all vertices v where deg(v) is the degree of v and ter(v) is the number of nets which have v as a tenninal. For nonstandard problems we can find a solution in time O(n(log n)2 + IUIZ) where U is the set of vertices v with deg(v) + ter(v) is odd.