Abstract
We present a new channel routing algorithm in the knock-knee mode that produces for dense problems area-optimal layouts with minimum total wire length and O(n) bends (n number of nets), where the total number of bends is at most d −2 (d density) more than the minimum. The running time is O(n). It thus improves the algorithm in [3] that determines area-optimal layouts with minimum total wire length in O(n2) time, where the number of bends is Ω(n2). Moreover, this is the first area-optimal layout algorithm with linear running time. The approach we use is completely different from all previously known algorithms. It is based on the notion of cycle graphs introduced in this paper.
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