An improved optimal algorithm for bubble-sorting-based non-Manhattan channel routing

It is well known that a non-Manhattan channel router always uses fewer routing tracks than a Manhattan router in a channel, To our knowledge, for a bubble-sorting-based non-Manhattan channel routing (BSNMCR) problem, Chaudhary's O(kn(2)) heuristic algorithm [8] and Chen's O(k(2)n) optimal algorithm [9] have been, respectively, proposed, where n is the number of terminals and k is the number of routing tracks in a channel. However, the time complexity of the two algorithms is in O(n(3)) time in the worst case. In this paper, based on optimality-oriented swap-direction selection in an optimal bubble-sorting solution, an improved optimal algorithm for a BSNMCR problem is proposed, and the time complexity of the proposed algorithm is proven to be in O(kn) time and in O(n(2)) time in the worst case.