Preferred Direction Steiner Trees

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Preferred Direction Steiner Trees

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by Mehmet Can Yildiz , Mehmet Can , Yildiz Patrick , Patrick H. Madden

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@MISC{Yildiz_preferreddirection,
    author = {Mehmet Can Yildiz and Mehmet Can and Yildiz Patrick and Patrick H. Madden},
    title = {Preferred Direction Steiner Trees},
    year = {}
}

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Abstract

Interconnect optimization for VLSI circuits has received wide attention. To model routing surfaces, multiple circuit layers are frequently abstracted as a single rectilinear plane, ignoring via costs, layer dependent routing costs, and congestion impact for routing in a particular direction. In this paper, we consider preferred direction multi-layer routing, which more closely models practical applications. We adapt a well known rectilinear planar Steiner tree heuristic, resulting in a new method to construct low cost Steiner trees under a realistic model. Our implementation is fast and effective, obtaining reductions in tree cost of 11% to 37% on average for random problems. Our results include a proof that the performance bound of Minimum Spanning Tree cost to Steiner Minimal Tree cost under this model is 2:1 (in contrast to 1.5:1 for planar problems). We adapt the Hanan grid to this model, and show that a Steiner tree which would be optimal under a planar formulation is suboptimal for the multi-layer preferred direction model. 1.

Keyphrases

direction steiner tree wide attention hanan grid new method realistic model particular direction interconnect optimization model practical application steiner minimal tree cost preferred direction multi-layer routing planar problem layer dependent routing cost performance bound congestion impact planar formulation steiner tree multiple circuit layer random problem multi-layer preferred direction model single rectilinear plane tree cost minimum spanning tree cost rectilinear planar steiner tree heuristic vlsi circuit low cost steiner tree

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