**A Note on the Density of the Multiple Subset Sum Problems**

*Yanbin Pan and Feng Zhang*

**Abstract: **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.

**Category / Keywords: **Lattice, Low-Density, Multiple Subset Sum Problem, Multiple Modular Subset Sum Problem.

**Date: **received 25 Sep 2011, last revised 17 Oct 2011

**Contact author: **panyanbin at amss ac cn

**Available format(s): **PDF | BibTeX Citation

**Version: **20111018:022234 (All versions of this report)

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