Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, June 09, 2005, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Christian Borgs (Microsoft Research & Univ. of Washington)

Proof of the local REM conjecture for number partitioning

The number partitioning problem is a classical combinatorial optimization problem: Given n numbers or weights, one is faced with the problem of partitioning this set of numbers into two subsets to mininize the discrepancy, defined as the absolute value of the difference in the total weights of the two subsets.

Here we consider random instances of this problem where the n numbers are i.i.d. random variables, and we study the distribution of the discrepancies and the correlations between partitions with similar discrepancy. In spite of the fact that the discrepancies of the 2^n-1 possible partitions are clearly correlated, a surprising recent conjecture states that the discrepancies near any given threshold become asymptotically independent, and that the partitions corresponding to these discrepancies become uncorrelated. In other words, the conjecture claims that near any fixed threshold, the cost function of the number partitioning problem behaves asymptotically like a random cost function.

In this talk, I describe our recent proof of this conjecture.

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