What algorithms do you know for beltway reconstruction? 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?
Paul Lemke Steven S. Skiena Warren D. Smith, Reconstructing Sets From Interpoint Distances, gave backtracking algorithm that runs in time $O(n^n \log n)$ for the beltway reconstruction problem. As far as I know, this is the best known. The exact complexity of the problem is not known. It is not known to be in $P$ and neither known to be $NP$-complete.