## Abstract

We study a path-planning problem amid a set O of obstacles in R^{2}, 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} log^{n} _{ε} ) a path of total cost at most (1 + ε) times the cost of the optimal path.

Original language | English |
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Article number | 46 |

Journal | ACM Transactions on Algorithms |

Volume | 14 |

Issue number | 4 |

DOIs | |

State | Published - Oct 2018 |

## Keywords

- Motion planning
- geometry
- approximation
- bicriteria objective

## ASJC Scopus subject areas

- Mathematics (miscellaneous)