Golomb ruler

In mathematics, a Golomb ruler, named after Solomon W. Golomb[?], is a set of marks at integer positions along an imaginary ruler such that no two pairs of marks are the same distance apart.

One practical use of Golomb rulers is in the design of phased array radio antennae such as radio telescopes. Antennae in an [0,1,4,6] Golomb ruler configuration can often be seen at cell sites[?].

The shortest Golomb rulers with a given number of points are referred to as optimal Golomb rulers.

distributed.net[?] is currently (2002) running a distributed massively parallel[?] search for optimal Golomb rulers.

Examples of Golomb rulers

• [0,1,3] optimal
• [0,1,3,7] not optimal
• [0,1,4,6] optimal
• [1,2,4,8,16,..(powers of 2)..] not optimal

References:

• Martin Gardner, "Mathematical games", Scientific American, March 1972, p. 108-112

External links:

• http://www.research.ibm.com/people/s/shearer/grule.html
• http://www.distributed.net/ogr/