Paper 2011/525

A Note on the Density of the Multiple Subset Sum Problems

Yanbin Pan and Feng Zhang


It is well known that the general subset sum problem is NP-complete. However, almost all subset sum problems with density less than $0.9408\ldots$ can be solved in polynomial time with an oracle that can find the shortest vector in a special lattice. In this paper, we give a similar result for the multiple subset sum problems which has $k$ subset sum problems with the same solution. Some extended versions of the multiple subset sum problems are also considered. In addition, a modified lattice is involved to make the analysis much simpler than before.

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Published elsewhere. Unknown where it was published
LatticeLow-DensityMultiple Subset Sum ProblemMultiple Modular Subset Sum Problem.
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panyanbin @ amss ac cn
2011-10-18: revised
2011-09-26: received
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      author = {Yanbin Pan and Feng Zhang},
      title = {A Note on the Density of the Multiple Subset Sum Problems},
      howpublished = {Cryptology ePrint Archive, Paper 2011/525},
      year = {2011},
      note = {\url{}},
      url = {}
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