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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: …
j_random_hacker's user avatar
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 …
j_random_hacker's user avatar
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 …
j_random_hacker's user avatar
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 …
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