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

