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I've faced the beltway reconstruction problem and I've developed a simple backtrack algorithm, what algorithms do you know for this problem?
Beltway Reconstruction Problem:
Assume there is a set of non-identical integers between 0 and N, we only have pairwise distances of points of that set mod N, How can we reconstruct the original set using this?

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cross-posted on Theoretical Computer Science. –  Kaveh Jul 9 '13 at 8:38
    
See also the MO question Difference Sets, which also discusses the beltway reconstruction problem. –  Joseph O'Rourke Jul 9 '13 at 10:42

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A relatively recent result for a sparse case can be found here (see Algorithm 2). It’s a probabilistic polynomial-time algorithm.

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Thanks. I've read these two papers: Reconstruction of Integers from Pairwise Distances & Reconstructing Sets From Interpoint Distances. Any other references? –  Mahdi Khosravi Jul 9 '13 at 7:16

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