Data structures and network algorithms
Data structures and network algorithms
A linear time algorithm with minimum link paths inside a simple polygon
Computer Vision, Graphics, and Image Processing
Rectilinear Shortest Paths and Minimum Spanning Trees in the Presence of Rectilinear Obstacles
IEEE Transactions on Computers
Computing the link center of a simple polygon
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
An efficient algorithm for link-distance problems
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Minimum-link paths among obstacles in the plane
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
An O(n log n) algorithm for computing the link center of a simple polygon
Discrete & Computational Geometry
Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
Finding Two Disjoint Paths Between Two Pairs of Vertices in a Graph
Journal of the ACM (JACM)
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
On Bends and Distances of Paths Among Obstacles in Two-Layer Interconnection Model
IEEE Transactions on Computers
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
The two disjoint path problem and wire routing design
Proceedings of the 17th Symposium of Research Institute of Electric Communication on Graph Theory and Algorithms
Constructing pairwise disjoint paths with few links
ACM Transactions on Algorithms (TALG)
Homotopic rectilinear routing with few links and thick edges
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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Smallest rectilinear paths are rectilinear paths with a minimum number of bends and with a minimum length simultaneously. In this paper, given two pairs of terminals within a rectilinear polygon, we derive an algorithm to find a pair of noncrossing rectilinear paths within the polygon such that the total number of bends and the total length are both minimized. Although a smallest rectilinear path between two terminals in a rectilinear polygon always exists, we show that such a smallest pair may not exist for some problem instances. In that case, the algorithm presented will find, among all noncrossing paths with a minimum total number of bends, a pair whose total length is the shortest, or find, among all noncrossing paths with a minimum total length, a pair whose total number of bends is minimized. We provide a simple linear time and space algorithm based on the fact that there are only a limited number of configurations of such a solution pair.