Two-sided single-detour untangling for bus routing

In this paper, based on the optimality of hierarchical bubble sorting, the problem of two-sided single-detour untangling for single-layer bus routing is firstly formulated. Compared with an optimal O(n
³
) algorithm for one-sided single-detour untangling without capacity consideration, an optimal O(n
²
) algorithm is proposed to solve the two-sided single-detour untangling problem without capacity consideration. For two-sided single-detour untangling with capacity consideration, an efficient O(n
²
) algorithm is proposed and the experimental results show that our proposed algorithm can successfully untangle all the twisted nets for the tested examples in less CPU time.