On some distance problems in fixed orientations
SIAM Journal on Computing
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
The X architecture: not your father's diagonal wiring
SLIP '02 Proceedings of the 2002 international workshop on System-level interconnect prediction
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Minimum Networks in Uniform Orientation Metrics
SIAM Journal on Computing
The Steiner Minimal Tree Problem in the lambda-Geormetry Plane
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
Rotationally optimal spanning and Steiner trees in uniform orientation metrics
Computational Geometry: Theory and Applications
Spanning graph-based nonrectilinear steiner tree algorithms
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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Let P be a set of n points in a metric space. A Steiner Minimal Tree (SMT) on P is a shortest network interconnecting P while a Minimum Spanning Tree (MST) is a shortest network interconnecting P with all edges between points of P. The Steiner ratio is the infimum over P of ratio of the length of SMT over that of MST. Steiner ratio problem is to determine the value of the ratio. In this paper we consider the Steiner ratio problem in uniform orientation metrics, which find important applications in VLSI design. Our study is based on the fact that lengths of MSTs and SMTs could be reduced through properly rotating coordinate systems without increasing the number of orientation directions. We obtain the Steiner ratios with |P| = 3 when rotation is allowed and some bounds of Steiner ratios for general case.