Abstract
The rectilinear shortest path problem can be stated as - given a set of m non-intersecting simple polygonal obstacles in the plane, find a shortest rectilinear (L 1) path from a point s to a point t which avoids all the obstacles. The path can touch an obstacle but does not cross it. This paper presents an algorithm with time complexity \(O(n+m(\lg{n})^{3/2})\), which is close to the known lower bound of \(\Omega(n+m\lg{m})\) for finding such a path. Here, n is the number of vertices of all the obstacles together. Our algorithm is of \(O(n+m(\lg{m})^{3/2})\) space complexity.
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Inkulu, R., Kapoor, S. (2007). Finding a Rectilinear Shortest Path in R 2 Using Corridor Based Staircase Structures. In: Arvind, V., Prasad, S. (eds) FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2007. Lecture Notes in Computer Science, vol 4855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77050-3_34
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DOI: https://doi.org/10.1007/978-3-540-77050-3_34
Publisher Name: Springer, Berlin, Heidelberg
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