Two nets occupy the same column the net at the top of

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two nets occupy the same column, the net at the top of the channel imposes a vertical constraint on the net at the bottom. For example, net 2 imposes a vertical constraint on net 4. Thus the interconnect for net 4 must use a track above net 2. (c) Horizontal-constraint graph. If the segments of two nets overlap, they are connected in the horizontal-constraint graph. This graph determines the global channel density. We can also define a horizontal constraint and a corresponding horizontal-constraint graph . If the trunk for net 1 overlaps the trunk of net 2, then we say there is a horizontal constraint between net 1 and net 2. Unlike a vertical constraint, a horizontal constraint has no direction. Figure 17.16 (c) shows an example of a horizontal constraint graph and shows a group of 4 terminals (numbered 3, 5, 6, and 7) that must all overlap. Since this is the largest such group, the global channel density is 4. If there are no vertical constraints at all in a channel, we can guarantee that the LEA will find the minimum number of routing tracks. The addition of vertical constraints transforms the restricted routing problem into an NP-complete problem. There is also an arrangement of vertical constraints that none of the algorithms based on the LEA can cope with. In Figure 17.17 (a) net 1 is above net 2 in the first column of the channel. Thus net 1 imposes a vertical constraint on net 2. Net 2 is above net 1 in the last column of the channel. Then net 2 also imposes a vertical constraint on net 1. It is impossible to route this arrangement using two routing layers with the restriction of using only one trunk for each net. If we construct the vertical-constraint graph for this situation, shown in Figure 17.17 (b), there is a loop or cycle between nets 1 and 2. If there is any such vertical-constraint cycle (or cyclic constraint ) between two or more nets, the LEA will fail. A dogleg router removes the restriction that each net can use only one track or trunk. Figure 17.17 (c) shows how adding a dogleg permits a channel with a cyclic constraint to be routed. FIGURE 17.17 The addition of a dogleg, an extra trunk, in the wiring of a net can resolve cyclic vertical constraints.
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The channel-routing algorithms we have described so far do not allow interconnects on one layer to run on top of other interconnects on a different layer. These algorithms allow interconnects to cross at right angles to each other on different layers, but not to overlap . When we remove the restriction that horizontal and vertical routing must use different layers, the density of a channel is no longer the lower bound for the number of tracks required. For two routing layers the ultimate lower bound becomes half of the channel density. The practical reasoning for restricting overlap is the parasitic overlap capacitance between signal interconnects. As the dimensions of the metal interconnect are reduced, the capacitance between adjacent interconnects on the same layer ( coupling capacitance ) is comparable to the capacitance of interconnects that overlap on different layers ( overlap capacitance ). Thus, allowing a short overlap between interconnects on
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  • Fall '15
  • prasad
  • Gate, The Land, Router, Hierarchical routing, nets, Global Routing, global router

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