Linear-Time Algorithms for Unspecified Routing in Grids (Extended Abstract)

Abstract

We give optimal algorithms for an unspecified channel routing problem which can be formulated as follows：Given a rectangular p × q grid, two sets of boundary vertices, S and T, of equal size, i.e., │S│=│T▕=n, the problem is to find n edge-disjoint or verter-disjoint paths joining vertices in S with vertices in T. For both edge-disjoint and verter-disjoint cases, we can test the existence of feasible solution in O(p + q) time and find the disjoint paths in O(pq) time.