Approximate Shortest Path through a Weighted Planar Subdivision
نویسندگان
چکیده
This paper presents an approximation algorithm for finding a shortest path between two points s and t in a weighted planar subdivision P . Each face f of P is associated with a weight wf , and the cost of travel along a line segment on f is wf multiplied by the Euclidean norm of that line segment. The cost of a path which traverses across several faces of the subdivision is the sum of the costs of travel along each face. Our algorithm progreeses the discretized shortest path wavefront from source s, and takes polynomial time in finding an ǫ-approximate shortest path.
منابع مشابه
Approximate shortest paths in moderately anisotropic regions
We want to find an approximate shortest path for a point robot moving in a planar subdivision. Each face of the subdivision is associated with a convex distance function that has the following property: its unit disk contains a unit Euclidean disk, and is contained in a Euclidean disk with radius ρ. Obstacles are allowed, so there can be regions that the robot is not allowed to enter. We give a...
متن کاملTriangulation Refinement and Approximate Shortest Paths in Weighted Regions
Let T be a planar subdivision with n vertices. Each face of T has a weight from [1, ρ] ∪ {∞}. A path inside a face has cost equal to the product of its length and the face weight. In general, the cost of a path is the sum of the subpath costs in the faces intersected by the path. For any ε ∈ (0, 1), we present a fully polynomial-time approximation scheme that finds a (1 + ε)-approximate shortes...
متن کاملThe Weighted Region Problem Is Defined as the Problem of Finding a Cost-optimal Path in a Weighted Planar Polygonal Subdivision. Searching for Paths on a Grid Representation Constr. Time
finding a cost-optimal path in a weighted planar polygonal subdivision. Searching for paths on a grid representation of the scene is fast and easy to implement. However, grid representations do not capture the exact geometry of the scene. Hence, grid paths can be inaccurate or might not even exist at all. Methods that work on an exact representation of the scene can approximate an optimal path ...
متن کاملAn Optimal Algorithm for L1 Shortest Paths Among Obstacles in the Plane (Draft)
We present an optimal Θ(n log n) algorithm for determining shortest paths according to the L1 (L∞) metric in the presence of disjoint polygonal obstacles in the plane. Our algorithm requires only linear O(n) space to build a planar subdivision (a Shortest Path Map) with respect to a fixed source point such that the length of a shortest path from the source to any query point can be reported in ...
متن کاملA note on the unsolvability of the weighted region shortest path problem
Let S be a subdivision of the plane into polygonal regions, where each region has an associated positive weight. The weighted region shortest path problem is to determine a shortest path in S between two points s, t ∈ R, where the distances are measured according to the weighted Euclidean metric—the length of a path is defined to be the weighted sum of (Euclidean) lengths of the sub-paths withi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1011.6498 شماره
صفحات -
تاریخ انتشار 2010