Routing a multi-terminal critical net: Steiner tree construction in the presence of obstacles

Ganley, Joseph L.; Cohoon, J. McGrath

doi:10.1109/iscas.1994.408768

Cited by 75 publications

(67 citation statements)

References 9 publications

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“…After the initialization steps (lines 1-3), line sweeping is performed from left to right. When the line meets the left boundary of o 1 , the interval [y 1,min , y 1,max ] is inserted into the interval set I as the "blocking information" (lines [5][6]. When the line meets the left boundary of o 2 , the interval [y 2,min , y 2,max ] is also inserted into the interval set I as the "blocking information" (lines [5][6].…”

Section: ) Oasg Construction Within a Regionmentioning

confidence: 99%

Efficient obstacle-avoiding rectilinear steiner tree construction

Lin

Chen

et al. 2007

Proceedings of the 2007 International Symposium on Physical Design

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Abstract-Given a set of pins and a set of obstacles on a plane, an obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) connects these pins, possibly through some additional points (called the Steiner points), and avoids running through any obstacle to construct a tree with a minimal total wirelength. The OARSMT problem becomes more important than ever for modern nanometer IC designs which need to consider numerous routing obstacles incurred from power networks, prerouted nets, IP blocks, feature patterns for manufacturability improvement, antenna jumpers for reliability enhancement, etc. Consequently, the OARSMT problem has received dramatically increasing attention recently. Nevertheless, considering obstacles significantly increases the problem complexity, and thus, most previous works suffer from either poor quality or expensive running time. Based on the obstacle-avoiding spanning graph, this paper presents an efficient algorithm with some theoretical optimality guarantees for the OARSMT construction. Unlike previous heuristics, our algorithm guarantees to find an optimal OARSMT for any two-pin net and many higher pin nets. Extensive experiments show that our algorithm results in significantly shorter wirelengths than all state-of-the-art works.

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Section: ) Oasg Construction Within a Regionmentioning

confidence: 99%

Efficient obstacle-avoiding rectilinear steiner tree construction

Lin

Chen

et al. 2007

Proceedings of the 2007 International Symposium on Physical Design

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“…It has been proved that there is an OARSMT composed only of segments and vertices in the escape graph. Moreover, some reduction tests [12], [14] can be applied to eliminate many vertices from the graph to produce a reduced escape graph, as shown in Fig. 9(b), while still guaranteeing the existence of an optimal solution.…”

Section: A Pruning Of Virtual Terminalsmentioning

confidence: 99%

“…Maze routing can give optimal solutions to two-terminal nets. Ganley et al [12] proposed the concept of escape graph and proved that there is an optimal solution composed only of 0278-0070/$26.00 c 2011 IEEE escape segments in the graph. A topology enumeration scheme is developed for the construction of optimal three-terminal and four-terminal OARSMTs.…”

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confidence: 99%

On the Construction of Optimal Obstacle-Avoiding Rectilinear Steiner Minimum Trees

Huang

Li²,

Young

2011

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

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Abstract-This paper presents an efficient method to solve the obstacle-avoiding rectilinear Steiner tree (OARSMT) problem optimally. Our work is developed based on the GeoSteiner approach in which full Steiner trees (FSTs) are first constructed and then combined into a rectilinear Steiner minimum tree (RSMT). We modify and extend the algorithm to allow obstacles in the routing region. For each routing obstacle, we first introduce four virtual terminals located at its four corners. We then give the definition of FSTs with blockages and prove that they will follow some very simple structures. Based on these observations, a twophase approach is developed for the construction of OARSMTs. In the first phase, we generate a set of FSTs with blockages. In the second phase, the FSTs generated in the first phase are used to construct an OARSMT. Finally, experiments on several benchmarks are conducted. Results show that the proposed method is able to handle problems with hundreds of terminals in the presence of multiple obstacles, generating an optimal solution in a reasonable amount of time.

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“…In terms of exact algorithms, Ganley et al [8] proposed a strong connection graph called escape graph for the OARSMT problem and prove that there is an optimal solution composed only of escape segments in the graph. Based on the escape graph, they proposed an algorithm to construct optimal three-terminal and fourterminal OARSMTs.…”

Section: Introductionmentioning

confidence: 99%

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

Huang

Young

2011

Proceedings of the 48th Design Automation Conference

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In this paper, we present an exact algorithm for the construction of obstacle-avoiding rectilinear Steiner minimum trees (OARSMTs) among complex rectilinear obstacles. This is the first work to propose a geometric approach to optimally solve the OARSMT problem among complex obstacles. The optimal solution is constructed by the concatenation of full Steiner trees (FSTs) among complex obstacles, which are proven to be of simple structures in this paper. The algorithm is able to handle complex obstacles including both convex and concave ones. Benchmarks with hundreds of terminals among a large number of obstacles are solved optimally in a reasonable amount of time.

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Routing a multi-terminal critical net: Steiner tree construction in the presence of obstacles

Cited by 75 publications

References 9 publications

Efficient obstacle-avoiding rectilinear steiner tree construction

Efficient obstacle-avoiding rectilinear steiner tree construction

On the Construction of Optimal Obstacle-Avoiding Rectilinear Steiner Minimum Trees

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

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