## Abstract

A constant-work-space algorithm has read-only access to an input array and may use only O(1) additional words of O(logn) bits, where n is the input size. We show how to triangulate a plane straight-line graph with n vertices in O(n^{2}) time and constant work-space. We also consider the problem of preprocessing a simple polygon P for shortest path queries, where P is given by the ordered sequence of its n vertices. For this, we relax the space constraint to allow s words of work-space. After quadratic preprocessing, the shortest path between any two points inside P can be found in O(n^{2}/s) time.

Original language | English |
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Pages (from-to) | 469-479 |

Number of pages | 11 |

Journal | Computational Geometry: Theory and Applications |

Volume | 47 |

Issue number | 3 PART B |

DOIs | |

Publication status | Published - 2014 Apr |

Externally published | Yes |

## Keywords

- Constant workspace
- Shortest path
- Simple polygon
- Space-time trade-off
- Triangulation

## ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics