## Adrian Dumitrescu

* “Recursive construction for
sliding disks”*

Digital print, 11" x 5", 2008.

Given a pair of start and target configurations, each consisting
of *n* pairwise disjoint disks in the plane, what is the minimum
number of moves that suffice for transforming the start
configuration
into the target configuration? In one move a disk slides in the
plane
without intersecting any other disk, so that its center moves
along an
arbitrary (open) continuous curve. One can easily show that
2*n* moves
always suffice, while the above construction shows pairs of
configurations
that require 2*n*-*o*(*n*) moves for this task, for every
sufficiently large *n*.
Disks in the start configuration are white, and disks in the target
configuration are shaded.

Adrian Dumitrescu, Associate Professor of Computer Science, Department of Computer Science,University of Wisconsin-Milwaukee, Milwaukee, USA

"Art could come from anywhere. One just wants to be careful and not
overlook it."

http://www.cs.uwm.edu/faculty/ad/