Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**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)

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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