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Optimal algorithms for bubble sort based non-Manhattan channel routing

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3 Author(s)
Chen, C.Y.R. ; Dept. of Electr. & Comput. Eng., Syracuse Univ., NY, USA ; Hou, C.Y. ; Singh, U.

It has been pointed out that, in many cases, results generated by non-Manhattan channel routers will be better than those generated by Manhattan routers. Non-optimal bubble sort based algorithms for non-Manhattan channel routing have been proposed in the literature by also allowing connections in the +45° and -45° directions. In this paper, optimal algorithms are proposed for the two-layer and three-layer non-Manhattan channel routing problems based on an identical problem formulation. The time complexities of our algorithms and the existing algorithm (which produces the best results so far) are O(K2 * N) and O(K * N2), respectively, where N is the number of terminals (i.e., the length) of the channel and N is the number of routing tracks (i.e., the height) in the channel. K is always less than N, and in most cases is much smaller than N. Clearly, a significant improvement in time complexity over the existing algorithm (which produces the best results so far) is achieved, while ensuring optimality

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Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on  (Volume:13 ,  Issue: 5 )