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 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.

Yield Analysis and Optimization

“…Methods to correct such situations include inserting jumpers in routes such that the maximum dangling route length is limited (see for example [68]). Diffusions diodes can also be inserted to provide a discharge path if space is available.…”

Optimal Jumper Insertion for Antenna Avoidance Considering Antenna Charge Sharing

“…The cells with "−" denote that no valid partitioning under the upper bound can be found with the obstacles presented. Note that the obstacle setting here is only for simplicity while the RatioPart algorithm can handle more general settings, e.g., the one in the work of Su et al [13] where the obstacles can forbid inserting jumpers on parts of an edge.…”

“…If for some reason, e.g., limited routing resource, such layer assignment is not feasible, a jumper must be inserted. Two more works [12], [13] focused on the jumper insertion problem itself. The latter one provided an exact algorithm to solve it in general routing trees with obstacles.…”

“…The latter one provided an exact algorithm to solve it in general routing trees with obstacles. In the works in [10], [12], and [13], a random discharging model was used and the upper bound on the total exposed antenna area connected to the gate oxides was controlled. In [11], although the same bound was controlled, Wu et al pointed out that when multiple sinks are presented, the algorithm will be conservative and not optimal.…”

An optimal simultaneous diode/jumper insertion algorithm for antenna fixing

“…Ho et al proposed full-chip routing with antenna avoidance [3]. These works [3,7,8] reduce the antenna effects during the routing stage while the works presented in [2,4,10,11] try to fix the antenna violations in the post-layout stage. Chen et al presented a heuristic to insert the diode under the wire with antenna violation [2].…”