Feasible offset and optimal offset for single-layer channel routing

The paper provides an efficient method to find all feasible offsets for a given separation in a VLSI channel routing problem in one layer. The prior literature considers this task only for problems with no single-sided nets. When single-sided nets are included, the worst-case solution time increases from Theta (n) to Omega (n/sup 2/), where n is the number of nets. But, if the number of columns c is O(n), one can solve the problem in time O(n/sup 1.5/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 or all single-sided nets are on one side to the channel. The authors also give improvements upon the naive approach for c not=O(n), including an algorithm with running time independent of c.<>