U. Fomeier, M. Kaufmann and A. Zelikovsky. Faster Approximation Algorithms for the Rectilinear Steiner Tree Problem. Lect. Notes in Comp. Sc. 762, 533-542, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....metric has been the most examined variant in electronic design automation, since IC fabrication technology typically mandates the use of only horizontal and vertical interconnect. The RST problem is NP hard [9] and much effort has been devoted to designing heuristic and approximation algorithms [1, 2, 3, 5, 10, 12, 13, 15, 16, 17, 25, 26, 27]. In an extensive survey of RST heuristics up to 1992 [14] the Batched Iterated 1 Steiner (BI1S) heuristic of Kahng and Robins [15] emerged as the clear winner with an average improvement over the MST on terminals of almost 11 . Subsequently, two other heuristics [3, 16] have been reported to ....

....vertex. Notably, the same reduction is the basis of a significant speed up in the running time of BI1S, and is currently incorporated in the implementation [19] Our vertex reduction is based on a simple empty rectangle test that has its roots in the work of Berman and Ramaiyer [2] see also [5, 26]) We ran experiments to compare our implementation of IRV against Robins implementation of BI1S [19] and against the GeoSteiner code of Warme, Winter, and Zachariasen [24] The results reported in Section 4 show that, on both random and real VLSI instances, our new heuristic produces on the ....

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U. Fossmeier, M. Kaufmann, and A. Zelikovsky. Faster approximation algorithms for the rectilinear Steiner tree problem, Discrete and Computational Geometry 18 (1997), pp. 93--109.

....the most examined variant in electronic design automation, since IC fabrication technology typically mandates the use of only horizontal and vertical interconnect. The RST problem is NP hard [9] and much effort has been devoted to designing heuristic and approximation algorithms [1] 2] 3] [5], 10] 13] 14] 16] 17] 18] 28] 29] 30] In an extensive survey of RST heuristics up to 1992 [15] the Batched Iterated 1 Steiner (BI1S) heuristic of Kahng and Robins [16] emerged as the clear winner with an average improvement over the MST on terminals of almost 11 . Subsequently, ....

.... Notably, the same reduction is the basis of a significant speed up in the running time of BI1S [11] and is currently incorporated in Robins implementation [20] Our vertex reduction is based on a simple empty rectangle test that has its roots in the work of Berman and Ramaiyer [2] see also [5], 29] We ran experiments to compare our implementation of IRV against Robins implementation of BI1S [20] and against the GeoSteiner code of Warme, Winter, and Zachariasen [27] The results reported in Section IV show that, on both random and real VLSI instances, our new heuristic produces on ....

[Article contains additional citation context not shown here]

U. Fossmeier, M. Kaufmann, and A. Zelikovsky. Faster approximation algorithms for the rectilinear Steiner tree problem, Discrete and Computational Geometry 18 (1997), pp. 93--109.

....metric has been the most examined variant in electronic design automation, since IC fabrication technology typically mandates the use of only horizontal and vertical interconnect. The RST problem is NP hard [8] and much effort has been devoted to designing heuristic and approximation algorithms [1, 2, 5, 11, 13, 15, 16, 18, 24, 25, 26]. In an extensive survey of RST heuristics up to 1992 [14] the Batched Iterated 1 Steiner (BI1S) heuristic of Kahng and Robins [15] emerged as the clear winner with an average improvement over the MST on terminals of almost 11 . Subsequently, two other heuristics [2, 16] have been reported to ....

....Steiner vertex. Notably, this observation also formed the basis of a significant speed up in the running time of BI1S [9] and is currently used in the implementation [19] Our vertex reduction is based on the empty rectangle test that has its roots in the work of Berman and Ramaiyer [1] see also [5, 25]) We ran experiments to compare our implementation of IRV against Robins implementation of BI1S [19] and against the GeoSteiner code of Warme, Winter, and Zachariasen [23] The results reported in Section 4 show that, on both random and real VLSI instances, our new heuristic produces on the ....

[Article contains additional citation context not shown here]

U. Fossmeier, M. Kaufmann, and A. Zelikovsky. Faster approximation algorithms for the rectilinear Steiner tree problem. Discrete and Computational Geometry 18 (1997), pp. 93--109.

....s 1:271s: 5 How Many Stars Have to be Considered To keep the time complexity small ( e.g. o(n 2 ) we have to restrict the number of stars where we look for our triples and quadruples. In this section we show that it is sufficient to regard only a linear number of triples and quadruples. In [9] we have shown analogous results just for triples: Lemma 8 It is sufficient to consider O(n) triples and this set can be constructed in time O(nlog 2 n) Since the only condition for our triples is that at the end of triple insertion there is no more triple with positive gain, we can use the ....

.... results just for triples: Lemma 8 It is sufficient to consider O(n) triples and this set can be constructed in time O(nlog 2 n) Since the only condition for our triples is that at the end of triple insertion there is no more triple with positive gain, we can use the triples constructed in [9]. So it remains to show that a linear number of quadruples is enough for our algorithm. From Fig. 1 we know that all quadruples have one of the shapes shown in Fig. 13 and Fig. 14. For a point p, p.x and p.y denote its x and y coordinate respectively. In the first part of this section we only ....

[Article contains additional citation context not shown here]

U. Fomeier, M. Kaufmann and A. Zelikovsky. Faster Approximation Algorithms for the Rectilinear Steiner Tree Problem. Lect. Notes in Comp. Sc. 762, 533-542, 1993.

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