An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles

Pankaj K. Agarwal; Kyle Fox; Oren Salzman; F. O.X. Kyle

doi:https://doi.org/10.1145/3230650

An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles

Pankaj K. Agarwal, Kyle Fox, Oren Salzman, F. O.X. Kyle

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We study a path-planning problem amid a set O of obstacles in R², in which we wish to compute a short path between two points while also maintaining a high clearance from O; the clearance of a point is its distance from a nearest obstacle in O. Specifically, the problem asks for a path minimizing the reciprocal of the clearance integrated over the length of the path. We present the first polynomial-time approximation scheme for this problem. Let n be the total number of obstacle vertices and let ε ∈ (0, 1]. Our algorithm computes in time O(ⁿ _ε ₂ ² logⁿ _ε ) a path of total cost at most (1 + ε) times the cost of the optimal path.

Original language	English
Article number	46
Journal	ACM Transactions on Algorithms
Volume	14
Issue number	4
DOIs	https://doi.org/10.1145/3230650
State	Published - Oct 2018

Keywords

Motion planning
approximation
bicriteria objective
geometry

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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title = "An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles",

abstract = "We study a path-planning problem amid a set O of obstacles in R2, in which we wish to compute a short path between two points while also maintaining a high clearance from O; the clearance of a point is its distance from a nearest obstacle in O. Specifically, the problem asks for a path minimizing the reciprocal of the clearance integrated over the length of the path. We present the first polynomial-time approximation scheme for this problem. Let n be the total number of obstacle vertices and let ε ∈ (0, 1]. Our algorithm computes in time O(n ε 2 2 logn ε ) a path of total cost at most (1 + ε) times the cost of the optimal path.",

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N2 - We study a path-planning problem amid a set O of obstacles in R2, in which we wish to compute a short path between two points while also maintaining a high clearance from O; the clearance of a point is its distance from a nearest obstacle in O. Specifically, the problem asks for a path minimizing the reciprocal of the clearance integrated over the length of the path. We present the first polynomial-time approximation scheme for this problem. Let n be the total number of obstacle vertices and let ε ∈ (0, 1]. Our algorithm computes in time O(n ε 2 2 logn ε ) a path of total cost at most (1 + ε) times the cost of the optimal path.

AB - We study a path-planning problem amid a set O of obstacles in R2, in which we wish to compute a short path between two points while also maintaining a high clearance from O; the clearance of a point is its distance from a nearest obstacle in O. Specifically, the problem asks for a path minimizing the reciprocal of the clearance integrated over the length of the path. We present the first polynomial-time approximation scheme for this problem. Let n be the total number of obstacle vertices and let ε ∈ (0, 1]. Our algorithm computes in time O(n ε 2 2 logn ε ) a path of total cost at most (1 + ε) times the cost of the optimal path.

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An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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