Shortest Paths in the Plane with Obstacle Violations
نویسندگان
چکیده
منابع مشابه
Shortest Paths in the Plane with Obstacle Violations
We study the problem of finding shortest paths in the plane among h convex obstacles, where the path is allowed to pass through (violate) up to k obstacles, for k ≤ h. Equivalently, the problem is to find shortest paths that become obstacle-free if k obstacles are removed from the input. Given a fixed source point s, we show how to construct a map, called a shortest k-path map, so that all dest...
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We address the problem of computing homotopic shortest paths in presence of obstacles in the plane. The problems on homotopy of the paths received attention very recently [3, 8]. We present two output-sensitive algorithms, for simple paths and non-simple paths. The algorithm for simple paths improves the previous algorithm [8]. The algorithm for non-simple paths achieves O(log n) time per outpu...
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We propose a new algorithm for a classical problem in plane computational geometry: computing a shortest path between two points in the presence of polygonal obstacles. Our algorithm runs in worst-case time O(nlog2n) and requires O(n1ogn) space, where n is the total number of vertices in the obstacle polygons. Our algorithm actually computes a planar map that encodes shortest paths from a fixed...
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Given a point s and a set of h pairwise disjoint polygonal obstacles of totally n vertices in the plane, we present a new algorithm for building an L1 shortest path map of size O(n) in O(T ) time and O(n) space such that for any query point t, the length of the L1 shortest obstacleavoiding path from s to t can be reported in O(log n) time and the actual shortest path can be found in additional ...
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In this paper an algorithm is presented to find a shortest path between two points in the plane amidst growing discs. That is, as the “point” moves through the plane, the discs grow at an a priori known rate. We present an O(n logn) algorithm and a fast implementation. The problem is motivated from robotics, where motion planning in dynamic environments is a great challenge. Our algorithm can b...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2020
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-020-00673-y