Algorithms for routing and testing routability of planar VLSI layouts
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
On continuous Homotopic one layer routing
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Single-layer wire routing and compaction
Single-layer wire routing and compaction
Line Simplification with Restricted Orientations
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Computing homotopic shortest paths in the plane
Journal of Algorithms
Constructing pairwise disjoint paths with few links
ACM Transactions on Algorithms (TALG)
River Routing Every Which Way, But Loose
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Computational Geometry: Theory and Applications
Computing homotopic shortest paths efficiently
Computational Geometry: Theory and Applications
Path simplification for metro map layout
GD'06 Proceedings of the 14th international conference on Graph drawing
Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming
IEEE Transactions on Visualization and Computer Graphics
Homotopic rectilinear routing with few links and thick edges
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
On d-regular schematization of embedded paths
Computational Geometry: Theory and Applications
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We study the problem of finding non-crossing minimum-link $\mathcal{C}$-oriented paths that are homotopic to a set of input paths in an environment with $\mathcal{C}$-oriented obstacles. We introduce a special type of $\mathcal{C}$-oriented paths--smooth paths--and present a 2-approximation algorithm that runs in O(n2 (n+logκ)+kin logn) time, where n is the total number of paths and obstacle vertices, kin is the total number of links in the input, and κ = |$\mathcal{C}$|. The algorithm also computes an O(κ)-approximation for general $\mathcal{C}$-oriented paths. As a related result we show that, given a set of $\mathcal{C}$-oriented paths with L links in total, non-crossing $\mathcal{C}$-oriented paths homotopic to the input paths can require a total of Ω(L logκ) links.