LEXA: a left-edge based crosstalk-minimum k-color permutation in VHV channels

Given the channel routing topology with k tracks, the problem of minimizing crosstalk is intractable, requiring O(k!) time even in the track-based permutation. In this paper, a new approach for track assignment enhancement, minimizing the signal crosstalk and defect areas between, nets, while preserving the number of tracks, is presented. The approach is to allow for the split "nets" to be permuted for better crosstalk minimization, rather than simply permuting the tracks. We present a graph-based heuristic running in O(k/sup 2/ek2/sup 2(/spl lambda/-1//spl circ/-/spl lambda/)) time to obtain a near-optimal solution, where K, is the minimum clique cover number in an associated interval graph G and e is the number of edges in G. Here the parameter /spl lambda/(/spl les/logk) provides a tradeoff between time complexity and solution quality. A noble split rainbow k-colour permutation algorithm is proposed based on a dynamic programming approach. Our experiments show a significant improvement; 6.4% (resp. 1%) for crosstalk and 32% (resp. 17%) for critical areas on dense channels, compared with an initial track assignment (resp. the track permutation of the initial track assignment). Our algorithm can also be applied to the lower power application, such that power dissipation due to crosstalk is minimized by enduring that wires carrying high activity signals are placed sufficiently far from the other wires.