TY - GEN

T1 - Maximum overhang (extended abstract)

AU - Paterson, Mike

AU - Peres, Yuval

AU - Thorup, Mikkel

AU - Winkler, Peter

AU - Zwick, Uri

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=58449116651&partnerID=8YFLogxK

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:58449116651

SN - 9780898716474

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 756

EP - 765

BT - Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms

T2 - 19th Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 20 January 2008 through 22 January 2008

ER -