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

Date and Time: Thursday, April 03, 2025, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Simon Weber

Finding Fixpoints of l_p Contraction Maps (Query-)Efficiently

This talk continues where Sebastian's talk on Tuesday left off: While he gave examples of problems reducing to finding (approximate) fixpoints of contraction maps with regards to different l_p-norms, I present our polynomial-query algorithm for this problem. Our algorithm achieves the same bound as the algorithm of Chen, Li, and Yannakakis for the l_\infty (max-norm) case, but works for ALL l_p norms for p>=1. Our approach is inspired by the centerpoint theorem from computational geometry. We generalize this famous theorem from the Euclidean setting to the l_p norm setting, which then yields a conceptually very simple algorithm for the contraction fixpoint problem.

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