on your mark...
Golomb rulers were discovered
by Solomon W. Golomb, a mathematics professor with an interest in coding, combinational
analysis, and mathematical puzzles. In fact, his interest and contributions
to the Scientific American "Mathematical Games" led to the existence
of Golomb Rulers. ("distributed.net: Project OGR) Golomb rulers are numbers in such an order that
each pair of numbers has a unique difference from all other pairs. A Golomb
ruler with only three marks would be 0-1-4. The distances between each of the
numbers are 1, 3, and 4. An optimal Golomb ruler with four marks is 0-1-4-6.
The distances between each of those numbers are 1, 2, 3, 4, 5, 6. Thus, the
marks have the most unique differences but the ruler is short in length. The
length is six, since six is the total distance from 0-6. However, Golomb rulers
are usually characterized by their differences; the above ruler would be 0-1-3-2.
When the rulers are written this way, the lengths can be found by adding all
of the differences.
Optimal Golomb rulers may
appear to be simple number patterns, but they are incredibly useful. Optimal
Golomb rulers — also referred to as OGR — are used in numerous fields of study,
such as laser technology, crystallography, and radio astronomy. They can even
be used in cryptography. The Internet hadn't been exposed to a Golomb ruler
distributed computing project until a now-defunct group created programs called
GARSP and GVANT. (Garry) Although this OGR groupšs efforts were somewhat
in vain- they didn't find any new optimal rulers; they only proved that the
current 21, 22, and 23 mark optimal Golomb rulers were, in fact, optimal- they
opened the possibility for distributed computing techniques to search for a
larger optimal ruler.
©2000 Team DC (Thinkquest Team C007645). Hosted by ThinkQuest.