On minimum-bend single row routing

The objective function of the problem is to minimize the number of doglegs (or bends) per net. The approach is based on graph-theoretic representation in which an instance of the single row routing problem is represented by three graphs: an overlap graph, a containment graph, and an interval graph. Using this graph representation, three algorithms are developed. It is shown that the algorithms have very tight performance bounds. In particular, it is proved that the maximum number of doglegs per net is bounded by O(k), where k is the size of the maximum clique in a certain graph representing the problem