Feasible Offset an Optimal Offset for Single-Layer Channel Routing

This paper provides an eficient method t o find all feasible offsets f o r a given separation in a VLSI channel routing problem in one layer. The prior literature considers this task only f o r problenis with no single-sided nets. When single-sided nets are included, the worst-case solution time increases from Q(n) to C2(ii2), where 11 is the number of nets. But we show that if the number of columns c is O(n) , we can solve the problem in time O ( I ~ ~ . ~ lg n ) , which improves upon a “naive” O(cn) approach. As a corollary of this result, the same time bound suffices to find the optimal offset (the one that minimizes separation). Better running times are obtained when there are no two-sided nets o r all single-sided nets are on one side of the channel. W e also give iriiproveiiients upon the naive approach for c # O(ii), including an algorithm with running time independent of c .