Algorithms for Routing in Planar Graphs

Michael Becker, Kurt Mehlhorn

Abstract: A routing problem is given by a planar graph G= (V, E) with a given embedding into the plane and a set Ne of nets. A net is a pair of points on the boundary of the infinite face. The goal is to find a set of pairwise edge-disjoint paths connecting the terminals of the various nets. We assume that the degree of every vertex not on the boundary of the infinite face is even and call such routing problems half-even. We show that one can decide in time O(bn) whether a half-even problem is solvable and that a solution can be constructed in time O(n 2). Here n=¦V¦ and b is the number of vertices on the boundary of the infinite face. If the routing problem is even, i.e. every cut has even free capacity, and G is a subgraph of the planar grid then a solution can be found in time O(n 3/2).