## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Tuesday, December 05, 2006, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Justus Schwartz

## The Santa Claus Problem in a Probabilistic Setting

We consider the scheduling formulation of the well known Santa Claus problem where $n$ processes have to be scheduled on $m$ machines without preemption. The goal is to maximize the minimum load. In our setting we assume that the expected processing time of each job is known, but the actual duration is determined after scheduling the jobs. We show that if the jobs have exponentially distributed processing times, and the ratio between the largest and the smallest expectation is at most $n/\log^3 n$, a simple greedy strategy has expected competitive ratio 1. On the other hand, we give an instance with ratio $n$ such that every algorithm has expected competitive ratio $\Omega(\sqrt{m})$.

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