Paper Info
Title
Approximation of octilinear steiner trees constrained by hard and soft obstacles
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 log2n) 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(n3) time, and (3) a (1.55 + ε)–approximation of the octilinear Steiner tree problem in the presence of soft rectangular obstacles
Year
DOI
Venue
2006
10.1007/11785293_24
SWAT
Keywords
Field
DocType
novel octilinear,steiner tree,octilinear steiner tree problem,large steiner tree,steiner tree problem,soft rectangular obstacle,soft obstacle,hard octilinear obstacle,octilinear steiner tree,vlsi design,shortest octilinear steiner tree,steiner trees,connected component,approximation algorithms,computational geometry,polynomial time
Discrete mathematics,Approximation algorithm,Data structure,Obstacle,Combinatorics,Polynomial,Vertex (geometry),Computer science,Steiner tree problem,Tree (data structure),Connected component
Conference
Volume
ISSN
ISBN
4059
0302-9743
3-540-35753-X
Citations 
PageRank 
References 
2
0.38
25
Authors
2
Name
Order
Citations
PageRank
Matthias Müller-hannemann149758.17
Anna Schulze291.57