### Abstract

In this paper we present results from analytical and experimental investigations into the performance of divide & conquer algorithms for determining Pareto points in multi-dimensional data sets of size n and dimension d. The focus in this work is on the worst-case, where all points are Pareto, but extends to problem sets where only a partial subset of the points is Pareto. Analysis supported by experiment shows that the number of comparisons is bounded by two different curves, one that is O(n (log n)∧(d-2)), and the other that is O(n∧log 3). Which one is active depends on the relative values of n and d. Also, the number of comparisons is very sensitive to the structure of the data, varying by orders of magnitude for data sets with the same number of Pareto points.

Original language | English (US) |
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Title of host publication | Collection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference |

Pages | 264-274 |

Number of pages | 11 |

State | Published - Dec 1 2004 |

Event | Collection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference - Albany, NY, United States Duration: Aug 30 2004 → Sep 1 2004 |

### Publication series

Name | Collection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference |
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Volume | 1 |

### Other

Other | Collection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference |
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Country | United States |

City | Albany, NY |

Period | 8/30/04 → 9/1/04 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

}

*Collection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference.*Collection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, vol. 1, pp. 264-274, Collection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, NY, United States, 8/30/04.

**Analysis of an algorithm for identifying pareto points in multi-dimensional data sets.** / Yukish, Michael Andrew; Simpson, Timothy William.

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

TY - GEN

T1 - Analysis of an algorithm for identifying pareto points in multi-dimensional data sets

AU - Yukish, Michael Andrew

AU - Simpson, Timothy William

PY - 2004/12/1

Y1 - 2004/12/1

N2 - In this paper we present results from analytical and experimental investigations into the performance of divide & conquer algorithms for determining Pareto points in multi-dimensional data sets of size n and dimension d. The focus in this work is on the worst-case, where all points are Pareto, but extends to problem sets where only a partial subset of the points is Pareto. Analysis supported by experiment shows that the number of comparisons is bounded by two different curves, one that is O(n (log n)∧(d-2)), and the other that is O(n∧log 3). Which one is active depends on the relative values of n and d. Also, the number of comparisons is very sensitive to the structure of the data, varying by orders of magnitude for data sets with the same number of Pareto points.

AB - In this paper we present results from analytical and experimental investigations into the performance of divide & conquer algorithms for determining Pareto points in multi-dimensional data sets of size n and dimension d. The focus in this work is on the worst-case, where all points are Pareto, but extends to problem sets where only a partial subset of the points is Pareto. Analysis supported by experiment shows that the number of comparisons is bounded by two different curves, one that is O(n (log n)∧(d-2)), and the other that is O(n∧log 3). Which one is active depends on the relative values of n and d. Also, the number of comparisons is very sensitive to the structure of the data, varying by orders of magnitude for data sets with the same number of Pareto points.

UR - http://www.scopus.com/inward/record.url?scp=20344395146&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=20344395146&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:20344395146

SN - 1563477165

SN - 9781563477164

T3 - Collection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

SP - 264

EP - 274

BT - Collection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

ER -