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Given two sets of nonnegative integer numbers:

$X = {x_1, x_2, ... x_n}$ $Y = {y_1, y_2, ... y_m}$

Need to find partition of $X$ on $m$ disjoint subsets, such as sum of elements in $i$-th subset equal to $y_i$.

This generalization of Subset sum problem, which is known to be NP-Complete. One of the probable way of solving is to reduce it to system of integer linear equalities. But it's even more general and really hard to solve task. May be one has some fresh ideas?

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You might synchronize your indices. Gerhard "Ask Me About System Design" Paseman, 2012.03.28 –  Gerhard Paseman Mar 28 '12 at 20:55
you may want to post this on cs.stackexchange.com –  Kaveh Apr 18 '12 at 3:42
I have several questions about this problem. I have already had a decision procedure for this problem, but I call it multi-target subset sum problem. It is my research topic. I wonder that where did you encounter this problem or any application about this. Maybe we can discuss it here or in email. Thank you! My email: dokelung@gmail.com –  user25450 Aug 21 '12 at 5:42

1 Answer 1


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This paper is directly available at or.deis.unibo.it/alberto/mssp_g_f.ps –  Barry Cipra Oct 27 '12 at 13:10

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