### Abstract

We show that the region lit by a point fight source inside a simple n-gon after at most k reflections off the boundary has combinatorial complexity O(n^{2k}), for any k > 1. A lower bound of Ω((n/k)^{2k}) is also established which matches the upper bound for any fixed k. A simple near-optimal algorithm for computing the illuminated region is presented, which runs in O(n^{2k} log n) time and O(n^{2k}) space for any k>1.

Original language | English (US) |
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Title of host publication | Algorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings |

Publisher | Springer Verlag |

Pages | 284-295 |

Number of pages | 12 |

Volume | 1097 |

ISBN (Print) | 3540614222, 9783540614227 |

State | Published - 1996 |

Event | 5th Scandinavian Workshop on Algorithm Theory, SWAT 1996 - Reykjavik, Iceland Duration: Jul 3 1996 → Jul 5 1996 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1097 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 5th Scandinavian Workshop on Algorithm Theory, SWAT 1996 |
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Country | Iceland |

City | Reykjavik |

Period | 7/3/96 → 7/5/96 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Algorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings*(Vol. 1097, pp. 284-295). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1097). Springer Verlag.

**Visibility with multiple reflections.** / Aronov, Boris; Davis, Alan R.; Dey, Tamal K.; Pal, Sudebkumar P.; Chithra Prasad, D.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Algorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings.*vol. 1097, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1097, Springer Verlag, pp. 284-295, 5th Scandinavian Workshop on Algorithm Theory, SWAT 1996, Reykjavik, Iceland, 7/3/96.

}

TY - GEN

T1 - Visibility with multiple reflections

AU - Aronov, Boris

AU - Davis, Alan R.

AU - Dey, Tamal K.

AU - Pal, Sudebkumar P.

AU - Chithra Prasad, D.

PY - 1996

Y1 - 1996

N2 - We show that the region lit by a point fight source inside a simple n-gon after at most k reflections off the boundary has combinatorial complexity O(n2k), for any k > 1. A lower bound of Ω((n/k)2k) is also established which matches the upper bound for any fixed k. A simple near-optimal algorithm for computing the illuminated region is presented, which runs in O(n2k log n) time and O(n2k) space for any k>1.

AB - We show that the region lit by a point fight source inside a simple n-gon after at most k reflections off the boundary has combinatorial complexity O(n2k), for any k > 1. A lower bound of Ω((n/k)2k) is also established which matches the upper bound for any fixed k. A simple near-optimal algorithm for computing the illuminated region is presented, which runs in O(n2k log n) time and O(n2k) space for any k>1.

UR - http://www.scopus.com/inward/record.url?scp=21344439275&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344439275&partnerID=8YFLogxK

M3 - Conference contribution

SN - 3540614222

SN - 9783540614227

VL - 1097

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 284

EP - 295

BT - Algorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings

PB - Springer Verlag

ER -