### Abstract

The Multidimensional Assignment Problem (MAP) is a higher-dimensional version of the Linear Assignment Problem that arises in the areas of data association, target tracking, resource allocation, etc. This paper elucidates the question of asymptotical behavior of the expected optimal value of the large-scale MAP whose assignment costs are independent identically distributed random variables with a prescribed probability distribution. We demonstrate that for a broad class of continuous distributions the limiting value of the expected optimal cost of the MAP is determined by the location of the left endpoint of the support set of the distribution, and construct asymptotical bounds for the expected optimal cost.

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

Pages (from-to) | 525-551 |

Number of pages | 27 |

Journal | Mathematical Programming |

Volume | 109 |

Issue number | 2-3 |

DOIs | |

State | Published - Mar 1 2007 |

Externally published | Yes |

### Keywords

- Asymptotical analysis
- Convergence bounds
- Expected optimal value
- Multidimensional assignment problem
- Random assignment problem

### ASJC Scopus subject areas

- Software
- Mathematics(all)

## Fingerprint Dive into the research topics of 'Asymptotic behavior of the expected optimal value of the multidimensional assignment problem'. Together they form a unique fingerprint.

## Cite this

*Mathematical Programming*,

*109*(2-3), 525-551. https://doi.org/10.1007/s10107-006-0036-x