Rectilinear Shortest Paths and Minimum Spanning Trees in the Presence of Rectilinear Obstacles
IEEE Transactions on Computers
Rectilinear shortest paths through polygonal obstacles in O(n(logn)2) time
SCG '87 Proceedings of the third annual symposium on Computational geometry
A faster approximation algorithm for the Steiner problem in graphs
Information Processing Letters
Reducing the Steiner problem in a normal space
SIAM Journal on Computing
Rectilinear paths among rectilinear obstacles
Discrete Applied Mathematics
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
The X architecture: not your father's diagonal wiring
SLIP '02 Proceedings of the 2002 international workshop on System-level interconnect prediction
Estimation of wirelength reduction for λ-geometry vs. manhattan placement and routing
Proceedings of the 2003 international workshop on System-level interconnect prediction
The Steiner Minimal Tree Problem in the lambda-Geormetry Plane
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
Obstacle-Avoiding Euclidean Steiner Trees in the Plane: An Exact Algorithm
ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
An Exact Algorithm for the Uniformly-Oriented Steiner Tree Problem
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Constructing exact octagonal steiner minimal trees
Proceedings of the 13th ACM Great Lakes symposium on VLSI
A new paradigm for general architecture routing
Proceedings of the 14th ACM Great Lakes symposium on VLSI
Efficient octilinear Steiner tree construction based on spanning graphs
Proceedings of the 2004 Asia and South Pacific Design Automation Conference
Highly scalable algorithms for rectilinear and octilinear Steiner trees
ASP-DAC '03 Proceedings of the 2003 Asia and South Pacific Design Automation Conference
Improving linear programming approaches for the steiner tree problem
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
Hardness and approximation of octilinear steiner trees
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
A near linear time approximation scheme for Steiner tree among obstacles in the plane
Computational Geometry: Theory and Applications
A near linear time approximation scheme for steiner tree among obstacles in the plane
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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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