### Abstract

We demonstrate that the linear multidimensional assignment problem with iid random costs is polynomially e{open}-approximable almost surely (a. s.) via a simple greedy heuristic, for a broad range of probability distributions of the assignment costs. Specifically, conditions on discrete and continuous distributions of the cost coefficients, including distributions with unbounded support, have been established that guarantee convergence to unity in the a. s. sense of the cost ratio between the greedy solution and optimal solution. The corresponding convergence rates have been determined.

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

Pages (from-to) | 153-164 |

Number of pages | 12 |

Journal | Optimization Letters |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2011 |

Externally published | Yes |

### Fingerprint

### Keywords

- Approximability
- Convergence almost surely
- Greedy heuristic
- Multidimensional assignment problem

### ASJC Scopus subject areas

- Control and Optimization

### Cite this

**On optimality of a polynomial algorithm for random linear multidimensional assignment problem.** / Krokhmal, Pavlo A.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On optimality of a polynomial algorithm for random linear multidimensional assignment problem

AU - Krokhmal, Pavlo A.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - We demonstrate that the linear multidimensional assignment problem with iid random costs is polynomially e{open}-approximable almost surely (a. s.) via a simple greedy heuristic, for a broad range of probability distributions of the assignment costs. Specifically, conditions on discrete and continuous distributions of the cost coefficients, including distributions with unbounded support, have been established that guarantee convergence to unity in the a. s. sense of the cost ratio between the greedy solution and optimal solution. The corresponding convergence rates have been determined.

AB - We demonstrate that the linear multidimensional assignment problem with iid random costs is polynomially e{open}-approximable almost surely (a. s.) via a simple greedy heuristic, for a broad range of probability distributions of the assignment costs. Specifically, conditions on discrete and continuous distributions of the cost coefficients, including distributions with unbounded support, have been established that guarantee convergence to unity in the a. s. sense of the cost ratio between the greedy solution and optimal solution. The corresponding convergence rates have been determined.

KW - Approximability

KW - Convergence almost surely

KW - Greedy heuristic

KW - Multidimensional assignment problem

UR - http://www.scopus.com/inward/record.url?scp=78650732811&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650732811&partnerID=8YFLogxK

U2 - 10.1007/s11590-010-0198-6

DO - 10.1007/s11590-010-0198-6

M3 - Article

AN - SCOPUS:78650732811

VL - 5

SP - 153

EP - 164

JO - Optimization Letters

JF - Optimization Letters

SN - 1862-4472

IS - 1

ER -