| 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) Proof of the local REM conjecture for number partitioningThe 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 2n-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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