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^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^{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≠O(n), including an algorithm with running time independent of c.