Date: 9 Dec 1985 09:08:12 EST (Mon) From: Dan Hoey To: ALAN at MIT-MC.ARPA Subject: Re: Attractive nuisances appear regularly in Scientific American. I should have known you couldn't resist finding yet more efficient rulers, and lo, there is an ALAN;. RULER here. Well, you can probably guess I couldn't resist either. So far I've pushed the lower bound for 14-mark rulers up to 122. But eliminating 121 took a little over 3 cpu-days (68010, C), and it seems to double each time, so I'm probably not going to get much farther. I took a somewhat different approach from the strategy given the article. I add marks from both the left and from the right. This lets me quickly eliminate some large distances as being unavailable. Then I have a neat cutoff for detecting that too many of the small distances have been used up, which I'll bore you with on request. I have some ideas that might yield fruit, that I haven't implemented. For instance, suppose mark x has been selected, and marks x+d and x+2d are open. Well, marks x+d and x+2d can't be both selected. If x+3d is unavailable for some reason, then distance d is not available from mark x+2d. If this elimination can be done enough times, we be able to eliminate mark x+2d from consideration. This might speed things up if the bookkeeping isn't too slow. Just wanted to know you're not alone. Let me know what you find. Dan