Suboptimal algorithm for a wire routing problem

Yang, Y.; Wing, O.

doi:10.1109/tct.1972.1083538

Cited by 30 publications

(10 citation statements)

References 5 publications

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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%

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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Section: A Pruning Of Virtual Terminalsmentioning

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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“…We do not reproduce the various authors' descriptions of each algorithm that we mention here, since it is very easy to see from the high-level classification that these algorithms are indeed in C. Algorithms which follow a greedy Kruskal- 8], are members of C, since using only point-point connections will build an MST, and the optional rerouting is then used to induce edge overlaps. Interestingly, exponential-time methods can also fall into the class C, e.g., the suboptimal branch-and-bound method of Yang and Wing [21]. Theorem 1 implies that all of these methods have the same worstcase error bound as the simple MST.…”

Section: Kruskal-steinermentioning

confidence: 99%

On the performance bounds for a class of rectilinear Steiner tree heuristics in arbitrary dimension

Kahng

Robins

1992

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

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Abstract-We give a family of examples on which a large class C of "minimum spanning tree-based'' rectilinear Steiner tree heuristics has performance ratio arbitrarily close to 3/2 times optimal. The class C contains many published heuristics whose worst-case performance ratio: were previously unknown. Of particular interest is that C contains two heuristics whose worst-case ratios had been conjectured to be bounded away from 3/2, and our construction also points out an incorrect claim of optimality for one of these heuristics. Our examples also force worst-possible behavior in a number of heuristics outside C. The construction generalizes to d dimensions, where the heuristics will have performance ratio of at least (2d -l / d ) ; this improves the previous lower bound on performance ratio in arbitrary dimension.

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“…Hanan [7] proved that there is a rectilinear Steiner minimal tree which is a subset of the grid graph. Yang and Wing [14] further proved that there is a rectilinear Steiner minimal tree which is a subset of the grid graph within Rconv(S).…”

Section: Terminologymentioning

confidence: 99%

A linear-time algorithm to construct a rectilinear Steiner minimal tree fork-extremal point sets

Richards

Salowe

1992

Algorithmica

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Suboptimal algorithm for a wire routing problem

Cited by 30 publications

References 5 publications

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

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

On the performance bounds for a class of rectilinear Steiner tree heuristics in arbitrary dimension

A linear-time algorithm to construct a rectilinear Steiner minimal tree fork-extremal point sets

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