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.
展开▼
机译：在本文中，我们研究了在一般布线（Steiner /生成树）树上插入跳线的问题，该树在布线和/或布局后阶段具有避开/固定天线的障碍。我们将用于天线避免/固定的跳线插入公式化为砍树问题，并提出了针对一般砍树问题的 first 最优算法。我们表明，砍树问题表现出最优子结构和贪婪选择的性质。有了这些属性，我们提出了使用数量最少的 O （（ V + D ）lg D ）次最佳跳线插入算法。跳线，以避免/修复带有 V 顶点和 D 障碍物的Steiner /生成树上的天线冲突。实验结果证明了该算法的优越性和有效性。
展开▼
