Approximation of Rectilinear Steiner Trees with Length Restrictions on Obstacles

Müller‐Hannemann, Matthias; Peyer, Sven

doi:10.1007/978-3-540-45078-8_19

Cited by 13 publications

(14 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, the currently strongest approximation guarantee by Robins and Zelikovsky for the Steiner tree problem in graphs implies a (1.55 + ε)-approximation for this problem. This matches the best known guarantees for the rectilinear case [MP03].…”

Section: Introductionsupporting

confidence: 86%

See 1 more Smart Citation

Approximation of Octilinear Steiner Trees Constrained by Hard and Soft Obstacles

Müller‐Hannemann

Schulze

2006

Algorithm Theory – SWAT 2006

Self Cite

View full text Add to dashboard Cite

Abstract. The novel octilinear routing paradigm (X-architecture) in VLSI design requires new approaches for the construction of Steiner trees. In this paper, we consider two versions of the shortest octilinear Steiner tree problem for a given point set K of terminals in the plane: (1) a version in the presence of hard octilinear obstacles, and (2) a version with rectangular soft obstacles. The interior of hard obstacles has to be avoided completely by the Steiner tree. In contrast, the Steiner tree is allowed to run over soft obstacles. But if the Steiner tree intersects some soft obstacle, then no connected component of the induced subtree may be longer than a given fixed length L. This kind of length restriction is motivated by its application in VLSI design where a large Steiner tree requires the insertion of buffers (or inverters) which must not be placed on top of obstacles. For both problem types, we provide reductions to the Steiner tree problem in graphs of polynomial size with the following approximation guarantees. Our main results are (1) a 2-approximation of the octilinear Steiner tree problem in the presence of hard rectilinear or octilinear obstacles which can be computed in O(n log 2 n) time, where n denotes the number of obstacle vertices plus the number of terminals, (2) a (2 + ε)-approximation of the octilinear Steiner tree problem in the presence of soft rectangular obstacles which runs in O(n 3 ) time, and (3) a polynomial time (1.55 + ε)-approximation of the octilinear Steiner tree problem in the presence of soft rectangular obstacles.

show abstract

Section: Introductionsupporting

confidence: 86%

“…Müller-Hannemann and Peyer [MP03] showed that the rectilinear Steiner tree problem in the presence of soft obstacles can be 2-approximated in O(n 2 log n) time, where n denotes the number of terminals plus the number of obstacle vertices. They also presented a (1.55 + ε)-approximation for rectangular obstacles.…”

Section: Introductionmentioning

confidence: 99%

Approximation of Octilinear Steiner Trees Constrained by Hard and Soft Obstacles

Müller‐Hannemann

Schulze

2006

Algorithm Theory – SWAT 2006

Self Cite

View full text Add to dashboard Cite

show abstract

“…Based on the definition of the extended Hanan grid, this grid contains the original Hanan grid [2] and the Escape graph [16]. However, an optimal solution to the LRSMT problem does not always lie in the extended Hanan grid [6]. Evidently, this conclusion also applies to the RSMT-RERR problem.…”

Section: Introductionmentioning

confidence: 72%

“…1(c), and results in a trade-off between total wire length and slew constraints over obstacles. In 2003, Muller-Hannemann et al [6] proposed a simplified model called the length-restricted Steiner minimum tree (LRSMT) problem. In this model, any connected component of a solution over an obstacle must be shorter than a given length restriction L. These researchers used a modified distance network heuristic (DNH) [11] to construct a feasible solution to LRSMT.…”

Section: Introductionmentioning

confidence: 99%