### Abstract

We study the problem of cutting a set of rods (line segments in ℝ^{3}) into fragments, using a minimum number of cuts, so that the resulting set of fragments admits a depth order. We prove that this problem is NP-complete, even when the rods have only three distinct orientations. We also give a polynomial-time approximation algorithm with no restriction on rod orientation that computes a solution of size O(τ logτ log logτ), where τ is the size of an optimal solution.

Original language | English (US) |
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Title of host publication | Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 1241-1248 |

Number of pages | 8 |

State | Published - 2008 |

Event | 19th Annual ACM-SIAM Symposium on Discrete Algorithms - San Francisco, CA, United States Duration: Jan 20 2008 → Jan 22 2008 |

### Other

Other | 19th Annual ACM-SIAM Symposium on Discrete Algorithms |
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Country | United States |

City | San Francisco, CA |

Period | 1/20/08 → 1/22/08 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 1241-1248)

**Cutting cycles of rods in space : Hardness and approximation.** / Aronov, Boris; De Berg, Mark; Gray, Chris; Mumford, Elena.

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

*Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms.*pp. 1241-1248, 19th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, United States, 1/20/08.

}

TY - GEN

T1 - Cutting cycles of rods in space

T2 - Hardness and approximation

AU - Aronov, Boris

AU - De Berg, Mark

AU - Gray, Chris

AU - Mumford, Elena

PY - 2008

Y1 - 2008

N2 - We study the problem of cutting a set of rods (line segments in ℝ3) into fragments, using a minimum number of cuts, so that the resulting set of fragments admits a depth order. We prove that this problem is NP-complete, even when the rods have only three distinct orientations. We also give a polynomial-time approximation algorithm with no restriction on rod orientation that computes a solution of size O(τ logτ log logτ), where τ is the size of an optimal solution.

AB - We study the problem of cutting a set of rods (line segments in ℝ3) into fragments, using a minimum number of cuts, so that the resulting set of fragments admits a depth order. We prove that this problem is NP-complete, even when the rods have only three distinct orientations. We also give a polynomial-time approximation algorithm with no restriction on rod orientation that computes a solution of size O(τ logτ log logτ), where τ is the size of an optimal solution.

UR - http://www.scopus.com/inward/record.url?scp=58449134854&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58449134854&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9780898716474

SP - 1241

EP - 1248

BT - Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms

ER -