Maximum overhang (extended abstract)

Mike Paterson*, Yuval Peres, Mikkel Thorup, Peter Winkler, Uri Zwick

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


How far can a stack of n identical blocks be made to hang over the edge of a table? The question dates back to at least the middle of the 19th century and the answer to it was widely believed to be of order logn. However, at SODA'06, Paterson and Zwick constructed n-block stacks with overhangs of order n 1/3. Here we complete the solution to the overhang problem, and answer Paterson and Zwick's primary open question, by showing that order n 1/3 is best possible. At the heart of the argument is a lemma (possibly of independent interest) showing that order d3 non-adaptive coinflips are needed to propel a discrete random walk on the number line to distance d. We note that our result is not a mainstream algorithmic result, yet it is about the solution to a discrete optimization problem. Moreover, it illustrates how methods founded in theoretical computer science can be applied to a problem that has puzzled some mathematicians and physicists for more than 150 years.

Original languageEnglish
Title of host publicationProceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms
Number of pages10
StatePublished - 2008
Event19th Annual ACM-SIAM Symposium on Discrete Algorithms - San Francisco, CA, United States
Duration: 20 Jan 200822 Jan 2008

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Conference19th Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CitySan Francisco, CA


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