### Abstract

Given a two dimensional, non-overlapping layout of convex and non-convex polygons, compaction can be thought of as simulating the motion of the polygons as a result of applied 'forces.' Compaction can be modeled as a motion of the polygons that reduces the value of some linear functional on their positions. Optimal compaction, planning a motion that finds the global minimum reachable value, is shown to be NP-complete. We give a compaction algorithm that finds a local minimum by direct calculation of the new polygon positions via linear programming. We also consider the related problem of separating overlapping polygons using a minimal amount of motion and show it to be NP-complete. A locally optimum version of this problem is solved using a slight modification of the compaction algorithm. The compaction algorithm and the separation algorithm have been applied to marker making: the task of packing polygonal pieces on a sheet of cloth of fixed width so that total length is minimized. The compaction algorithm has improved cloth utilization of human generated pants markers. The separation algorithm together with a database of human-generated markers can be used to automatically generate markers that are close to human performance.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the 9th Annual Symposium on Computational Geometry |

Editors | Anon |

Publisher | Publ by ACM |

Pages | 153-162 |

Number of pages | 10 |

ISBN (Print) | 0897915828 |

State | Published - 1993 |

Externally published | Yes |

Event | Proceedings of the 9th Annual Symposium on Computational Geometry - San Diego, CA, USA Duration: May 19 1993 → May 21 1993 |

### Other

Other | Proceedings of the 9th Annual Symposium on Computational Geometry |
---|---|

City | San Diego, CA, USA |

Period | 5/19/93 → 5/21/93 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the 9th Annual Symposium on Computational Geometry*(pp. 153-162). Publ by ACM.

**Compaction algorithm for non-convex polygons and its application.** / Li, Zhenyu; Milenkovic, Victor.

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

*Proceedings of the 9th Annual Symposium on Computational Geometry.*Publ by ACM, pp. 153-162, Proceedings of the 9th Annual Symposium on Computational Geometry, San Diego, CA, USA, 5/19/93.

}

TY - GEN

T1 - Compaction algorithm for non-convex polygons and its application

AU - Li, Zhenyu

AU - Milenkovic, Victor

PY - 1993

Y1 - 1993

N2 - Given a two dimensional, non-overlapping layout of convex and non-convex polygons, compaction can be thought of as simulating the motion of the polygons as a result of applied 'forces.' Compaction can be modeled as a motion of the polygons that reduces the value of some linear functional on their positions. Optimal compaction, planning a motion that finds the global minimum reachable value, is shown to be NP-complete. We give a compaction algorithm that finds a local minimum by direct calculation of the new polygon positions via linear programming. We also consider the related problem of separating overlapping polygons using a minimal amount of motion and show it to be NP-complete. A locally optimum version of this problem is solved using a slight modification of the compaction algorithm. The compaction algorithm and the separation algorithm have been applied to marker making: the task of packing polygonal pieces on a sheet of cloth of fixed width so that total length is minimized. The compaction algorithm has improved cloth utilization of human generated pants markers. The separation algorithm together with a database of human-generated markers can be used to automatically generate markers that are close to human performance.

AB - Given a two dimensional, non-overlapping layout of convex and non-convex polygons, compaction can be thought of as simulating the motion of the polygons as a result of applied 'forces.' Compaction can be modeled as a motion of the polygons that reduces the value of some linear functional on their positions. Optimal compaction, planning a motion that finds the global minimum reachable value, is shown to be NP-complete. We give a compaction algorithm that finds a local minimum by direct calculation of the new polygon positions via linear programming. We also consider the related problem of separating overlapping polygons using a minimal amount of motion and show it to be NP-complete. A locally optimum version of this problem is solved using a slight modification of the compaction algorithm. The compaction algorithm and the separation algorithm have been applied to marker making: the task of packing polygonal pieces on a sheet of cloth of fixed width so that total length is minimized. The compaction algorithm has improved cloth utilization of human generated pants markers. The separation algorithm together with a database of human-generated markers can be used to automatically generate markers that are close to human performance.

UR - http://www.scopus.com/inward/record.url?scp=0027830221&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027830221&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0897915828

SP - 153

EP - 162

BT - Proceedings of the 9th Annual Symposium on Computational Geometry

A2 - Anon, null

PB - Publ by ACM

ER -