Optimal point location in a monotone subdivision
SIAM Journal on Computing
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
On shortest paths in polyhedral spaces
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Computational geometry.
Proximity and reachability in the plane.
Proximity and reachability in the plane.
Rectilinear Shortest Paths and Minimum Spanning Trees in the Presence of Rectilinear Obstacles
IEEE Transactions on Computers
Gross motion planning—a survey
ACM Computing Surveys (CSUR)
Shortest paths in the plane with polygonal obstacles
Journal of the ACM (JACM)
Monotonicity of rectilinear geodesics in d-space (extended abstract)
Proceedings of the twelfth annual symposium on Computational geometry
Single step current driven routing of multiterminal signal nets for analog applications
DATE '00 Proceedings of the conference on Design, automation and test in Europe
Routing using implicit connection graphs [VLSI design
VLSID '96 Proceedings of the 9th International Conference on VLSI Design: VLSI in Mobile Communication
A nearly optimal algorithm for finding L1shortest paths among polygonal obstacles in the plane
ESA'11 Proceedings of the 19th European conference on Algorithms
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We address ourselves to an instance of the Shortest Path problem with obstacles where a shortest path in the Manhattan (or L1) distance is sought between two points (source and destination) and the obstacles are n disjoint rectangles with sides parallel to the coordinate axes. A plane sweep technique is applied rather than the graph theoretic approach frequently used in the literature. We show that there has to be a path of minimum length between the two given points which is monotone in at least one of x or y directions. Then we present an algorithm of time complexity &Ogr;(n log n) for constructing that path and show that our algorithm is optimal.Lastly, we address the query form of this problem in which given a source point and n obstacles, after &Ogr;(n log n) time for preprocessing, a shortest path from the source point to a query point avoiding all the obstacles can be reported in &Ogr;(t + log n) time, where t is the number of turns on the path.