An optimal jumper insertion algorithm for antenna avoidance/fixing on general routing trees with obstacles

Abstract

We study in this paper the problem of jumper insertion on general routing (Steiner/spanning) trees with obstacles for antenna avoidance/fixing at the routing and/or post-layout stages. We formulate the jumper insertion for antenna avoidance/fixing as a tree-cutting problem and present the firstoptimal algorithm for the general tree-cutting problem. We show that the tree-cutting problem exhibits the properties of optimal substructures and greedy choices. With these properties, we present an O((V+D) lg D)-time optimal jumper insertion algorithm that uses the least number of jumpers to avoid/fix the antenna violations on a Steiner/spanning tree with V vertices and D obstacles. Experimental results show the superior effectiveness and efficiency of our algorithm.