Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, October 12, 2004, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Alex Souza-Oftermatt

Recent Progress in Stochastic Knapsack

In this talk we consider the following stochastic variant of the Knapsack problem. We are given a finite set N = {1, 2, ..., n} of objects, where each object j yields a profit p_j and has a weight w_j. Profits are drawn from a probability distribution and weights are specified by an adversary. In addition, the adversary also chooses the capacity of a knapsack. The problem is to choose objects as to maximise total profit while not violating the capacity constraint. In the recent work of Beier and Vöcking 'Random Knapsack in Expected Polynomial Time' [STOC '03] and 'Probabilistic Analysis of Knapsack Core Algorithms' [SODA '04] substantial progress on this problem was made.

The conclusion is that the above problem can be solved to optimality in expected time O(n polylog(n)). The key ingredients are two algorithms; an enumeration algorithm and a so-called core algorithm. Combination of these yields the claimed bound. In this talk we will present the main ideas behind these algorithms, their combination and sketch their analysis.

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