Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
A linear time algorithm with minimum link paths inside a simple polygon
Computer Vision, Graphics, and Image Processing
Joint triangulations and triangulation maps
SCG '87 Proceedings of the third annual symposium on Computational geometry
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Optimal link path queries in a simple polygon
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Minimal link visibility paths inside a simple polygon
Computational Geometry: Theory and Applications
On compatible triangulations of simple polygons
Computational Geometry: Theory and Applications
Finding a minimum weight K-link path in graphs with Monge property and applications
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Proceedings of the twelfth annual symposium on Computational geometry
Rectilinear paths among rectilinear obstacles
Discrete Applied Mathematics
Constructing piecewise linear homeomorphisms of simple polygons
Journal of Algorithms
The Smallest Pair of Noncrossing Paths in a Rectilinear Polygon
IEEE Transactions on Computers
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
A Polynomial Solution to the Undirected Two Paths Problem
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Algorithms for Finding Non-Crossing Paths with Minimum Total Length in Plane Graphs
ISAAC '92 Proceedings of the Third International Symposium on Algorithms and Computation
Finding Shortest Non-Crossing Rectilinear Paths in Plane Regions
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Homotopic rectilinear routing with few links and thick edges
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
GD'12 Proceedings of the 20th international conference on Graph Drawing
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Let P be a simple polygon and let {(u1, u′1), (u2, u′2),…,(um, u′m)} be a set of m pairs of distinct vertices of P, where for every distinct i, j ≤ m, there exist pairwise disjoint (nonintersecting) paths connecting ui to u′i and uj to u′j. We wish to construct m pairwise disjoint paths in the interior of P connecting ui to u′i for i = 1, …,m, with a minimal total number of line segments. We give an approximation algorithm that constructs such a set of paths using O(M) line segments in O(n log m + M log m) time, where M is the number of line segments in the optimal solution and n is the size of the polygon.