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## Random Assignment with Integer Costs (2001)

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### Other Repositories/Bibliography

Venue: | COMBIN. PROBAB. COMPUT |

Citations: | 2 - 0 self |

### Citations

1321 | Probability: Theory and Examples - Durrett - 1996 |

201 |
Volgenant A. A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing
- Jonker
- 1987
(Show Context)
Citation Context ...xpected minimal cost. Besides that, we look at the variance of the expected minimal cost, as well as the row rank distribution. To solve the realizations, we used an algorithm by Jonker and Volgenant =-=[6]-=-. In a recent survey [4], it came out as one of the fastest available algorithms for 5scost 1.835 1.83 1.825 1.82 1.815 1.81 1.805 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 dimension Figure... |

69 |
On the solution of the random link matching problems
- Mézard, Parisi
- 1987
(Show Context)
Citation Context ...costs are i.i.d. exponential (mean 1) there are strong conjectures for the more general case of k-assignment from a m × n cost matrix. Let Z∗ (k, m, n) denote the minimal cost. Mézard and Parisi [=-=8], [9], conjectur-=-ed that lim n→∞ E(Z∗ (n, n, n)) = π 2 /6. This was proven by Aldous [1]. Parisi [11] has also conjectured that E(Z ∗ n� 1 (n, n, n)) = , i2 which was improved by Coppersmith and Sorkin [3] ... |

58 | Asymptotics in the random assignment problem. Probability Theory and Related Fields - Aldous - 1992 |

58 | The ζ(2) limit in the random assignment problem. Random Structures and Algorithms - Aldous - 2001 |

55 | The ζ(2) limit in the random assignment problem
- Aldous
(Show Context)
Citation Context ...neral case of k-assignment from a m × n cost matrix. Let Z∗ (k, m, n) denote the minimal cost. Mézard and Parisi [8], [9], conjectured that lim n→∞ E(Z∗ (n, n, n)) = π 2 /6. This was proven=-= by Aldous [1]. Parisi [11-=-] has also conjectured that E(Z ∗ n� 1 (n, n, n)) = , i2 which was improved by Coppersmith and Sorkin [3] to E(Z ∗ (k, m, n)) = � 1 (m − i)(n − j) . i+j<k 1 i=1sThe last conjecture was pro... |

51 | Constructive Bounds and Exact Expectations For the Random
- Coppersmith, Sorkin
- 1999
(Show Context)
Citation Context ... [9], conjectured that lim n→∞ E(Z∗ (n, n, n)) = π 2 /6. This was proven by Aldous [1]. Parisi [11] has also conjectured that E(Z ∗ n� 1 (n, n, n)) = , i2 which was improved by Coppersmith =-=and Sorkin [3] to E(Z ∗ (-=-k, m, n)) = � 1 (m − i)(n − j) . i+j<k 1 i=1sThe last conjecture was proven by Alm and Sorkin [2] for k ≤ 4, k = m = 5, and k = m = n = 6. Linusson and Wästlund [7] extended this to k ≤ 6, ... |

42 |
Replicas and optimization
- Mézard, Parisi
- 1985
(Show Context)
Citation Context ... the costs are i.i.d. exponential (mean 1) there are strong conjectures for the more general case of k-assignment from a m × n cost matrix. Let Z∗ (k, m, n) denote the minimal cost. Mézard and Par=-=isi [8], [9], conj-=-ectured that lim n→∞ E(Z∗ (n, n, n)) = π 2 /6. This was proven by Aldous [1]. Parisi [11] has also conjectured that E(Z ∗ n� 1 (n, n, n)) = , i2 which was improved by Coppersmith and Sorkin... |

35 | An intermediate course in probability - Gut - 1995 |

31 |
Asymptotic properties of the random assignment problem
- Olin
- 1992
(Show Context)
Citation Context ...distribution has density h(x) = e−x (e −x − 1 + x) (1 − e −x ) 2 , 0 ≤ x < ∞. Theorem 1.3. lim n→∞ P (Ciπ(i) is the kth smallest element of the ith row in C) = 2 −k . Remark. In a=-= simulation study in [10]-=-, Olin noted that, even for as small dimensions as n = 50, the row rank distribution is surprisingly close to the above. 2 Coupling arguments In this section we will prove the following theorem. 2 isT... |

31 | A conjecture on random bipartite matching
- Parisi
- 1998
(Show Context)
Citation Context ...f k-assignment from a m × n cost matrix. Let Z∗ (k, m, n) denote the minimal cost. Mézard and Parisi [8], [9], conjectured that lim n→∞ E(Z∗ (n, n, n)) = π 2 /6. This was proven by Aldous [=-=1]. Parisi [11] has also co-=-njectured that E(Z ∗ n� 1 (n, n, n)) = , i2 which was improved by Coppersmith and Sorkin [3] to E(Z ∗ (k, m, n)) = � 1 (m − i)(n − j) . i+j<k 1 i=1sThe last conjecture was proven by Alm an... |

27 |
Algorithms and codes for dense assignment problems: the state of the art
- Dell’Amico, Toth
(Show Context)
Citation Context ...sides that, we look at the variance of the expected minimal cost, as well as the row rank distribution. To solve the realizations, we used an algorithm by Jonker and Volgenant [6]. In a recent survey =-=[4]-=-, it came out as one of the fastest available algorithms for 5scost 1.835 1.83 1.825 1.82 1.815 1.81 1.805 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 dimension Figure 1: Simulation results, ... |

19 | Exact expectations and distributions in the random assignment problem
- Alm, Sorkin
(Show Context)
Citation Context ... conjectured that E(Z ∗ n� 1 (n, n, n)) = , i2 which was improved by Coppersmith and Sorkin [3] to E(Z ∗ (k, m, n)) = � 1 (m − i)(n − j) . i+j<k 1 i=1sThe last conjecture was proven by Alm=-= and Sorkin [2] for -=-k ≤ 4, k = m = 5, and k = m = n = 6. Linusson and Wästlund [7] extended this to k ≤ 6, and k = m = n = 7. 1.1 Discrete variants We will study four discrete variants of the random assignment probl... |

16 | The probabilistic relationship between the assignment and asymmetric traveling salesman problems - Frieze, Sorkin - 2001 |

9 | A generalization of the random assignment problem
- Linusson, Wästlund
- 2000
(Show Context)
Citation Context ...y Coppersmith and Sorkin [3] to E(Z ∗ (k, m, n)) = � 1 (m − i)(n − j) . i+j<k 1 i=1sThe last conjecture was proven by Alm and Sorkin [2] for k ≤ 4, k = m = 5, and k = m = n = 6. Linusson and=-= Wästlund [7] e-=-xtended this to k ≤ 6, and k = m = n = 7. 1.1 Discrete variants We will study four discrete variants of the random assignment problem. Case I Each row in C is an independent random permutation of {1... |

1 | On the fluctuation in the random assignment problem - Lee, Su - 2002 |