Su, B.-Y.B.-Y.SuHu, J.J.HuYAO-WEN CHANG2018-09-102018-09-10200702780070http://www.scopus.com/inward/record.url?eid=2-s2.0-33947581705&partnerID=MN8TOARShttp://scholars.lib.ntu.edu.tw/handle/123456789/332284We 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 postlayout stages. We formulate the jumper insertion for antenna avoidance/fixing as a tree-cutting problem and present the first optimal 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. © 2007 IEEE.Antenna effect; Design for manufacturability; Physical design; Reliability; RoutingAntenna effect; Design for manufacturability; Physical design; Routing; Antennas; Collision avoidance; Computational complexity; Problem solving; Reliability; Trees (mathematics); Algorithmsjournal article10.1109/TCAD.2007.8923382-s2.0-33947581705WOS:000245190500010