Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, May 30, 2006, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Stefan Geisseler

Overhang

By M. Paterson and U. Zwick (ACM-SIAM Symposium on Discrete Algorithms (SODA'06))

How far off the edge of the table can we reach by stacking n identical blocks of length 1? A classical solution achieves an overhang of 1/2H_n, where H_n = ∑ⁿ_i=1 1/i ~ ln n is the n^th harmonic number, by stacking all the blocks one on top of another with the i^th block from the top displaced by 1/2i beyond the block below. This solution is widely believed to be optimal. We show that it is exponentially far from optimal by giving explicit constructions with an overhang of Ω(n^1/3). We also prove some upper bounds on the overhang that can be achieved. The stability of a given stack of blocks corresponds to the feasibility of a linear program and so can be efficiently determined.

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