Title: ILP-based Alleviation of Dense Meander Segments with Prioritized Shifting and Progressive Fixing in PCB Routing,
Abstract: Length-matching is an important technique to bal- ance delays of bus signals
in high-performance PCB routing. Existing routers, however, may generate very
dense meander segments. Signals propagating along these meander segments
exhibit a speedup effect due to crosstalk between the segments of the same
wire, thus leading to mismatch of arrival times even under the same physical
wire length. In this paper, we present a post-processing method to enlarge the
width and the distance of meander segments and hence distribute them more
evenly on the board so that crosstalk can be reduced. In the proposed
framework, we model the sharing of available routing areas after removing dense
meander segments from the initial routing, as well as the generation of relaxed
meander segments and their groups for wire length compensation. This model is
transformed into an ILP problem and solved for a balanced distribution of wire
patterns. In addition, we adjust the locations of long wire segments according
to wire priorities to swap free spaces toward critical wires that need much
length compensation. To reduce the problem space of the ILP model, we also
introduce a progressive fixing technique so that wire patterns are grown
gradually from the edge of the routing toward the center area. Experimental
results show that the proposed method can expand meander segments significantly
even under very tight area constraints, so that the speedup effect can be
alleviated effectively in high- performance PCB designs.