Boundary single-layer routing with movable terminals

The authors study a generalization of previous results on the boundary single-layer routing (BSLR) problem. In the BSLR problem, there is a planar graph, a collection of terminals on the boundary of the infinite face, and a set of multiterminal nets. A solution of BSLR consists of a set of vertex disjoint trees interconnecting the terminals belonging to the same (multiterminal) net. An algorithm, unifying and generalizing previous BSLR algorithms, to solve an arbitrary instance of BSLR, is presented. Problems involving slidable terminals (i.e. when terminals can slide within a certain range on the boundary) and permutable terminals (i.e. when positions of some terminals (going to the same gate) can be interchanged) are optimally solved. The proposed algorithm runs in O(e) time, where e is the number of edges in the input graph. The results are extended to handle gridless routing environments