An exact algorithm for the construction of rectilinear Steiner minimum trees among complex obstacles

Huang, Tao; Young, Evangeline F. Y.

doi:10.1145/2024724.2024762

Cited by 18 publications

(12 citation statements)

References 18 publications

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“…As we can see, (8), (9), and (10) are all strictly increasing function with respect to d. If we shift EF up (i.e. towards the source), d will decrease and thus the delays from A to B, C and D will all decrease.…”

Section: Internal Tree Structures In An Optimal Solutionmentioning

confidence: 92%

“…Therefore, although routing over obstacles is possible, one should be aware of the signal integrity issue and avoid routing long wires on top of obstacles that may lead to complicated post-routing electrical fixups. One way to tackle this problem is to construct an obstacle-avoiding rectilinear Steiner minimum tree (OARSMT) [4][5][6][7][8][9][10]. However, avoiding all obstacles may result in an unnecessary resource overhead.…”

Section: Introductionmentioning

confidence: 99%

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Construction of rectilinear Steiner minimum trees with slew constraints over obstacles

Huang

Young

2012

Proceedings of the International Conference on Computer-Aided Design

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This work studies the problem of finding a rectilinear Steiner minimum tree (RSMT) for a set of given terminals in the presence of obstacles. In modern VLSI designs, obstacles usually block the device layer and a fraction of metal layers. Therefore, routing wires on top of obstacles is possible. However, if a long wire is routed over an obstacle, there will be signal integrity problems because buffers cannot be placed on top of any obstacle. To tackle this problem, we impose slew constraints on the interconnects that are routed over an obstacle. This is called the obstacle-avoiding rectilinear Steiner minimum trees (OARSMT) problem with slew constraints over obstacles. In this paper, we first analyze an optimal solution to this problem and show that the tree structures over obstacles with slew constraints will follow some very simple forms. Based on this observation, we propose an algorithm to find an optimal solution embedded in the extended Hanan grid [1]. The solutions can guarantee the interconnect performance and avoid post-routing electrical fixups due to slew violations. We also show that our algorithm achieves over 800 times speedup and is able reduce nearly 5% routing resources on average in comparison with the state-of-the-art optimal OARSMT algorithm.

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Section: Internal Tree Structures In An Optimal Solutionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Construction of rectilinear Steiner minimum trees with slew constraints over obstacles

Huang

Young

2012

Proceedings of the International Conference on Computer-Aided Design

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“…Make-Set(p) 8 insert p into HV 9 while not all pin-vertices are in the same set 10 (u, v) ← Nearest Components(HV , HE, V , E) In [12], the authors had shown that the 3D-VG has O(|VS| log 2 |VS|) vertices and edges, and can be constructed in O(|VS| log 3 |VS|) time. One O(log |VS|) factor of the number of vertices, the number of edges, and the time complexity results from the depth of recursion for Step 2-Step 4 of the 3D-VG construction.…”

Section: It Is Clear That For Each Edge E Of T R(e) Is Valid In R(imentioning

confidence: 99%

“…However, as the IC technology significantly increases the density of an IC chip, a modern IC design contains more and more hard IP cores, macro blocks, and pre-routed nets, which are referred to as obstacles in the routing process. Therefore, the obstacle-avoiding RSMT (OARSMT) problem has become very important and received lots of attention recently [1]- [8].…”

Section: Introductionmentioning

confidence: 99%

An efficient algorithm for multi-layer obstacle-avoiding rectilinear Steiner tree construction

Liu

Chen

Lee

2012

Proceedings of the 49th Annual Design Automation Conference

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We consider the multi-layer obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) problem and propose a reduction to transform a multi-layer instance into a 3D instance. Based on the reduction we apply computational geometry techniques to develop an efficient algorithm, utilizing existing OARSMT heuristics. Experimental results show that our algorithm provides a solution with excellent quality and has a significant speed-up compared to previously known results.

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“…Therefore, the obstacle-avoiding RSMT (OARSMT) problem has become very important and received lots of attention recently [2]- [10].…”

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confidence: 99%

Efficient Multilayer Obstacle-Avoiding Rectilinear Steiner Tree Construction Based on Geometric Reduction

Liu

Lin

Chen

et al. 2014

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Given a set of pin-vertices, an obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) connects all the pin-vertices possibly through Steiner points using vertical and horizontal segments with the minimal wirelength and without intersecting any obstacle. To deal with multiple routing layers and preferred routing orientations, we consider the multilayer obstacle-avoiding rectilinear Steiner minimal tree (ML-OARSMT) problem and the obstacle-avoiding preferred direction Steiner tree (OAPD-ST) problem. First, we prove that the multilayer case is theoretically different from the 2D one, and propose a reduction to transform a multilayer instance into a 3D instance. Based on the reduction, we apply computational geometry techniques to develop an efficient algorithm, utilizing existing OARSMT heuristics, for the ML-OARSMT problem and the OAPD-ST problem. Furthermore, we develop an advanced Steiner point selection to avoid inferior Steiner points and to improve the solution quality. Experimental results show that our algorithm provides a solution with excellent quality and has a significant speed-up compared to previously known results.

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An exact algorithm for the construction of rectilinear Steiner minimum trees among complex obstacles

Cited by 18 publications

References 18 publications

Construction of rectilinear Steiner minimum trees with slew constraints over obstacles

Construction of rectilinear Steiner minimum trees with slew constraints over obstacles

An efficient algorithm for multi-layer obstacle-avoiding rectilinear Steiner tree construction

Efficient Multilayer Obstacle-Avoiding Rectilinear Steiner Tree Construction Based on Geometric Reduction

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