Talk:Golomb ruler

message: This page doesn't answer a query of mine.
Ok I can see it being used with large arrays of telescopes, but are there (or is there planned) arrays of 25 telescopes? 
I guess what I'm trying to ask is is there a need to find Golomb rulers of such high orders? I'm assuming there is if distributed.net is putting power behind it, but there is no clear reason on that either.
Smremde 13:53, 25 September 2006 (UTC)
replies: text: This page: http://faq.distributed.net/cache/134.html from the distributed.net site lists a few uses: "OGR's have many applications including sensor placements for X-ray crystallography and radio astronomy. Golomb rulers can also play a significant role in combinatorics, coding theory and communications." Someone with more of a clue might want to add a note to that effect. 62.79.64.148 04:43, 23 August 2007 (UTC)
thread_title: Practical applications

message: The table says it contains all optimal rulers of a given order:
maybe someone with more time to spare than I have right now could check which ones are perfect and come up with a way of distinguishing them?
—Phil | Talk 08:59, 14 November 2005 (UTC)
replies: text: It has been proven that no perfect Golomb ruler exists for five or more ticks., as we only list one ruler for each of 4 and below, I think it's clear. :) --Gmaxwell 00:06, 7 April 2006 (UTC)
thread_title: Perfect rulers in table 

message: As of 20:29, 22 September 2006 (UTC)
replies: text: I have created a new disambiguation page at OGR. --Ghewgill 01:00, 24 September 2006 (UTC)
thread_title:  Name conflict on "OGR" 

message: Say, you'd rewrite 0 1 4 10 18 23 25 as 25 24 21 15 7 2 0 by using 25 - x on each element, it would still be a Golomb ruler, right? Are there any standards on which version should be used?
Translation and reflection of a Golomb ruler are considered trivial, so the smallest mark is customarily put at 0 and the next mark at the smaller of its two possible values. or use the basic arithmetic: if two elements are x and y do what you said so x -> 25 - x and y -> 25 - y now check the differences: x - y and (25 - x) - (25 - y) = 25 - x - 25 + y = -x + y = y - x  which is still the same because this problem is about ABSOLUTE differences (and |x - y| = |y - x|, any map of X -> Constant -/+ X is a OGR if X is an OGR. 94.208.111.0 (talk) 20:24, 26 October 2008 (UTC)
thread_title:  Are Golomb rulers symmetric? 

message: Linear arrays of radio telescopes can in principle be configured according to the values of a Golomb ruler.  In practice, however, one of the most important properties of a telescope (its resolving power) is not consistent with the defining properties of the Golomb ruler.  If the configuration of a linear array radio telescope was determined by a Golomb ruler, then the telescope's resolution would be proportional to the maximum difference between elements of the ruler for which all differences less than it are also present.  The fact that Golomb ruler designs attempt to produce as large a maximum difference as possible makes them attractive for radio telecope designs.  The problem is that one of the defining property of the Golomb ruler is the requirement that no difference be generated by more than one pair of its elements.  In radio telescope parlance, these would be called redundant baselines.  The avoidance of redundant baselines is generally not considered a driving requirement in the design of radio telescope arrays, and the presence of redundancies would be considered perfectly acceptable if they enabled an improvement in resolving power.  For this reason, if a Golomb ruler were used to determine the placement of elements in a linear array of telescopes, it would in most cases be considered sub-optimal.  
A counterexample to the Golomb ruler with 10 elements illustrates this point.  The Golomb ruler has elements 
[0 1 6 10 23 26 34 41 53 55]
The maximum difference below which all differences are present is 35 (generated by 41 minus 6).  This is the maximum because all differences below 35 are present but there is no difference of 36.  An alternate configuration for a linear array of 10 radio telescopes is
[0 1 3 6 13 20 27 31 35 36]
The maximum difference in this case is 36, which is one more than the Golomb ruler and hence would produce a radio telescope with 36/35 times better resolution.  This alternate configuration does have some redundant baselines and so it would not qualify as a Golomb ruler.  But it would be the preferred configuration for most radio telescope designers.  
Large linear arrays radio telescopes for Earth environmental monitoring from aircraft have been built with 5, 10 and 14 elements.  In each case, the Golomb ruler design has not been used because it does not optimize the resolution.  Satellite versions of these telescopes with significantly larger numbers of elements are currently being designed that also do not use Golomb ruler configurations for the same reason.
There is one other practical reason why Golomb ruler configurations are generally considered sub-optimal for aircraft and satellite applications.  The maximum difference between all possible elements in the Golomb ruler is often much larger than the maximum difference below which all differences are present.  If the Golomb ruler configuration was used, the telescope would end up being much larger than it would have been if the maximum possible difference was the same as the maximum difference below which all differences are present.  The two 10 element configurations listed above illustrate this.  The Golomb ruler has a maximum difference of 55 whereas the alternate configuration has a maximum of 36.  A linear array based on the Golomb ruler would be 55/36 times larger and have slightly poorer resolution.  Since unnecessarily large structures on satellites are generally avoided whenever possible, a  telescope designer would be unlikely to chose the Golomb ruler configuration.  CR (talk) 17:28, 30 October 2008 (UTC)
thread_title:  Utility and limitations for radio telescope arrays 

message: In the external links, the link to "James B. Shearer's Golomb ruler pages" appears to no longer go directly to the indicated page, but to a generic page at IBM for their labs.  I suspect having this link on this page no longer offers any value, other than free advertising for IBM.  —Preceding unsigned comment added by 67.193.106.116 (talk) 14:52, 6 September 2010 (UTC)
thread_title:  Suggested Edits 

message: Is there something like ruler where a condition that no distance are coded twice can be relaxed? It could in principle bring more flexibility and possibly encode more distances using same number of marks.  —Preceding unsigned comment added by 91.213.255.7 (talk) 20:28, 3 May 2011 (UTC)
thread_title:  almost-Golomb ruler 

message: There's a page here with a program relating to Golomb rulers. Maybe we could add it somewhere?  — Preceding unsigned comment added by 82.23.61.36 (talk) 01:04, 2 March 2017 (UTC)
thread_title:  Example program 

message: I've removed the following deeply suspect claim from the article:
 Antennas in a [0,1,4,6] Golomb ruler configuration can often be seen at AM tower or cell sites.
Why would a broadcast antenna or cell tower, which are required to have omnidirectional coverage, use a phased array configuration? And why would it need to have a choice of six different spacings? Also, having browsed through several of the images of cell phone base stations to be found on Wikipedia, I found no examples of Golomb ruler configurations, which would seem to disprove the "often" part at the very least. (Not that finding something that did look like one would actually prove anything, of course, since there would be no evidence that the arrangement was deliberate.)
By the way, the text had previously been tagged as , but the tag was quietly removed - and an additional unsourced factoid inserted - without any discussion. Well, maybe now someone will discuss it.
I was tempted to remove the part about transformers too, but it at least seems plausible, so I left it in. But it really does need a reference. 88.144.54.111 (talk) 19:08, 9 April 2022 (UTC)
thread_title:  Dubious claim about cell phone antennas