On Bends and Distances of Paths Among Obstacles in Two-Layer Interconnection Model
IEEE Transactions on Computers
Approximation Algorithms for the Minimum Bends Traveling Salesman Problem
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Finding rectilinear least cost paths in the presence of convex polygonal congested regions
Computers and Operations Research
Algorithms and theory of computation handbook
Faster algorithms for minimum-link paths with restricted orientations
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
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Efficient algorithms are presented for finding rectilinear collision-free paths between two given points among a set of rectilinear obstacles. The results improve the time complexity of previous results for finding the shortest rectilinear path, the minimum-bend shortest rectilinear path, the shortest minimum-bend rectilinear path and the minimum-cost rectilinear path. For finding the shortest rectilinear path, a graph-theoretic approach is used and an algorithm is obtained with $O(m\log t+ t\log^{3/2} t)$ running time, where $t$ is the number of extreme edges of given obstacles and $m$ is the number of obstacle edges. Based on this result an $O(N\log N+(m+N)\log t + (t+N)\log^2 (t+N))$ running time algorithm for computing the $L_1$ minimum spanning tree of given $N$ terminals among rectilinear obstacles is obtained. For finding the minimum-bend shortest path, the shortest minimum-bend rectilinear path, and the minimum-cost rectilinear path, we devise a new dynamic-searching approach and derive algorithms that run in $O(m\log^2m)$ time using $O(m\log m)$ space or run in $O(m\log^{3/2}m)$ time and space.