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Optimal Golomb Rulers

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get set... go!

distributed.net screenshot

Fig. 1: Visit the OGR project's headquarters at distributed.net.

Distributed.net, a distributed computing group, showed interest in the search two years ago, but only began to make client software available earlier this year. Their goal is to find a shorter, more optimal ruler with 24 marks.

The OGR search is more complicated than its sister project, the RC5-64 search. The OGR search is systematic, and utilizes the existing optimal rulers. It starts off by placing a mark at a specific distance past the end of the ruler. This distance is tested against the distances of other marks; if there is another distance of the same length — a duplicate — the mark is moved to the right one unit and rechecked for duplicity. If the mark is too far to the right, making the total length longer than the current optimal ruler, the process is restarted. Whenever the total length of the new ruler is longer than the current optimal ruler, the new one wouldn't be optimal, which strays from the goal of the project. If the new mark satisfies the conditions, though, the search continues down the ruler to another mark. The next mark compares distances with a table of existing distances. With this table, the program does not need to check each new mark position; the positions can be based on the table of distances. (Hewgill)

Since the OGR search involves many calculations, most work-units take at least a few days to process. In OGR, work-units are called packets, and packets make up one stub. The time it takes to process the data will differ for each stub, since the stub depends on the number of nodes involved. Nodes are the smallest unit that OGR checks; most computers can check a million nodes each second. Thus, the more nodes involved, the processing time — as well as the likelihood of finding a new ruler — increases. ("distributed.net Faq-O-Matic")

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