## Abstract

We present several algorithms for computing the visibility polygon of a simple polygon P of n vertices (out of which r are reflex) from a viewpoint inside P, when P resides in read-only memory and only few working variables can be used. The first algorithm uses a constant number of variables, and outputs the vertices of the visibility polygon in O(nr̄) time, where r̄ denotes the number of reflex vertices of P that are part of the output. Whenever we are allowed to use O(s) variables, the running time decreases to O(nr2 ^{s}+n^{log2}r) (or O(nr2^{s}+nlogr) randomized expected time), where s∈O(logr). This is the first algorithm in which an exponential space-time trade-off for a geometric problem is obtained.

Original language | English |
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Pages (from-to) | 918-926 |

Number of pages | 9 |

Journal | Computational Geometry: Theory and Applications |

Volume | 47 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2014 Oct |

Externally published | Yes |

## Keywords

- Computational geometry
- Memory-constrained algorithms
- Simple polygon
- Time-space-trade-off visibility

## ASJC Scopus subject areas

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