# An algorithm for finding a non-trivial lower bound for channel routing

TL;DR: A deterministic polynomial time algorithm is proposed that computes a better and non-trivial lower bound on the number of tracks required for routing a channel without doglegging.

Abstract: Channel routing is a key problem in the physical design of VLSI chips. It is known that max(d max , v max ) is a lower bound on the number of tracks required in the reserved two-layer Manhattan routing model, where dmax is the channel density and vmax is the length of the longest path in the vertical constraint graph. In this paper we propose a deterministic polynomial time algorithm that computes a better and non-trivial lower bound on the number of tracks required for routing a channel without doglegging. This algorithm is also applicable for computing a lower bound on the number of tracks in the three-layer no-dogleg HVH routing as well as two- and three-layer restricted dogleg routing models.

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### Cites background or methods from "An algorithm for finding a non-triv..."

...This paper emphasizes on finding a better nontrivial lower bound than the earlier deterministic algorithm [9]....

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...Theorem 1: MIMETIC_LBOUND computes exact lower bound on the number of track requirement to route a channel, and result is better or at least equal to that found using LOWER_BOUND algorithm [9]....

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...Channel instance dmax vmax max(dmax, vmax) Lbound by our algorithm CPU time Best solution known [9] CH1 4 4 4 6 0....

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...The deterministic version of computing a nontrivial lower bound is presented in [9], that took time Ο(n) for a channel of n nets....

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...MIMETIC_LBOUND also provides result as good as earlier computed lower bound for Deutsch’s difficult example (DDE) [9]....

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