On some distance problems in fixed orientations
SIAM Journal on Computing
Minimum Networks in Uniform Orientation Metrics
SIAM Journal on Computing
On the location of Steiner points in uniformly-oriented Steiner trees
Information Processing Letters
An Exact Algorithm for the Uniformly-Oriented Steiner Tree Problem
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
The Y-Architecture for On-Chip Interconnect: Analysis and Methodology
Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
The Y-architecture: yet another on-chip interconnect solution
ASP-DAC '03 Proceedings of the 2003 Asia and South Pacific Design Automation Conference
Rotational steiner ratio problem under uniform orientation metrics
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
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We consider the problem of finding a minimum spanning and Steiner tree for a set of n points in the plane where the orientations of edge segments are restricted to λ uniformly distributed orientations, λ = 2, 3, 4,..., and where the coordinate system can be rotated around the origin by an arbitrary angle. The most important cases with applications in VLSI design arise when λ = 2 or λ = 4. In the former, so-called rectilinear case, the edge segments have to be parallel to one of the coordinate axes, and in the latter, so-called octilinear case, the edge segments have to be parallel to one of the coordinate axes or to one of the lines making 45° with the coordinate axes (so-called diagonals). As the coordinate system is rotated--while the points remain stationary--the length and indeed the topology of the minimum spanning or Steiner tree changes. We suggest a straightforward polynomial-time algorithm to solve the rotational minimum spanning tree problem. We also give a simple algorithm to solve the rectilinear Steiner tree problem in the rotational setting, and a finite time algorithm for the general Steiner tree problem with λ uniform orientations. Finally, we provide some computational results indicating the average savings for different values of n and λ both for spanning and Steiner trees.