tgl@a.sei.cmu.edu.UUCP (02/19/86)
I have found a 15-mark Golomb ruler which is shorter than the
best previously known according to the December Sci. Am. article.
It is
spaces: 3 1 18 32 10 6 11 13 15 8 21 5 7 2
marks: 0 3 4 22 54 64 70 81 94 109 117 138 143 150 152
This is of length 152, whereas the best previously known was 155.
This was found by an exhaustive search program running on a 68020.
It's still cranking along, and will be for quite a while yet.
I can state that there are no shorter 15-mark rulers having a space
of length 2 at either end...
tom lane
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ARPA: lane@{CMU-CS-A.ARPA|A.CS.CMU.EDU}
UUCP: ...!seismo!cmu-cs-a!laneminow@decvax.UUCP (Martin Minow) (02/22/86)
From March '86 Scientific American: "... during the Christmas Holidays, James B. Shearer of the IBM Thomas J. Watson Research Center programmed an idle computer to search exhaustively for rulers, and the computer has now turned up Golomb rulesr with 14 and 15 marks. The 14-mark Golumb ruler is 127 units long and has marks at 0, 5, 28, 38, 41, 49, 50, 68, 75, 92, 107, 121, 123, and 127. The 15-mark ruler is 151 units long and has marks at 0, 6, 7, 15, 28, 40, 51, 75, 89, 92, 94, 121, 131, 147, and 151. Shearer writes that he saved much computing time by assuming the middle mark on the ruler is to the left of the geometric middle." Quoted by Martin Minow decvax!minow
anthony@utcsstat.uucp (Anthony Ayiomamitis) (02/25/86)
Can someone briefly describe Golomb ruler data points once again?
I tried locating an earlier article on USENET that described them but did not
succeed. I hope to use this information to get my Apple to do some searching
for new solutions. Many thanks in advance.
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