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

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1 Author(s)
Jin-Tai Yan ; Comput. Syst. Res. Center, Nat. Chiao Tung Univ., Hsinchu, Taiwan

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(kn2) heuristic algorithm (1991) and Chen's O(k2n) optimal algorithm (1994) have been, respectively, proposed, where it 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(n3) 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(n2) time in the worst case

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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  (Volume:18 ,  Issue: 2 )