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
The Smallest Pair of Noncrossing Paths in a Rectilinear Polygon
IEEE Transactions on Computers
Computing homotopic shortest paths in the plane
Journal of Algorithms
Thick non-crossing paths and minimum-cost flows in polygonal domains
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
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
A mixed-integer program for drawing high-quality metro maps
GD'05 Proceedings of the 13th international conference on Graph Drawing
GD'12 Proceedings of the 20th international conference on Graph Drawing
Two-Sided boundary labeling with adjacent sides
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
On d-regular schematization of embedded paths
Computational Geometry: Theory and Applications
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We study the NP-hard problem of finding non-crossing thick minimum-link rectilinear paths which are homotopic to a set of input paths in an environment with rectangular obstacles. We present a 2-approximation that runs in $O(n^3 + k_{in} \log n + k_{out})$ time, where n is the total number of input paths and obstacles and kin and kout are the total complexities of the input and output paths. Our algorithm not only approximates the minimum number of links, but also simultaneously minimizes the total length of the paths. We also show that an approximation factor of 2 is optimal when using smallest paths as lower bound.