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 Hn = ∑i=1n 1/i ∼ Inn is the nth harmonic number, by stacking all the blocks one on top of another with the ith 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(n1/3). 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.
|Number of pages
|Published - 2006
|Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms - Miami, FL, United States
Duration: 22 Jan 2006 → 24 Jan 2006
|Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms
|22/01/06 → 24/01/06