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Questions about the NP-complete problem Subset Sum.
1
vote
Accepted
Can the subset sum problem work with an undefined set?
If you only have extra impurities, then the DECOMP program described in the following paper will efficiently solve the problem -- even if you only have an approximate mass difference $d$ to work with: …
1
vote
Unlimited use subset sum
If the $k_i$ are restricted to be positive integers (please clarify whether this is the case or not in your question), D.W.'s nice approach could give an invalid answer (i.e., an answer with some $k_i …
3
votes
Subset Sum With Interval Target
With negative integers permitted
Unlike the SSITP problem restricted to positive integers, when negative integers are permitted the problem is NP-complete. I'll show this by reduction from ordinary Su …
4
votes
Accepted
Subset Sum With Interval Target
With positive integers only
Consider the largest element $a_m$ in the input. We have the following cases:
$a_m \in [\lceil\frac{1}{2}T\rceil, \lfloor\frac{3}{4}T\rfloor]$. We can simply choose $\{a_m …