A Note on the Density of the Multiple Subset Sum Problems

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 . . . 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 problem which has k subset sum problems with the same solution. A modified lattice is involved to make the analysis much simpler than before. In addition, some extended versions of the multiple subset sum problem are also considered.

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