## ⓘ Subset sum problem

The subset sum problem is an important problem of computer science. It can be stated as follows: Given a set of integers, does any subset of them sum to zero? For example, given the set { -7, -3, -2, 5, 8}, the answer is yes because the subset { -3, -2, 5} sums to zero. The problem is NP-Complete. It can be reformulated to the 3SAT. An alternative statement of this problem is, given a set of numbers and an integer x determine whether or not there exist a subset that sums up to x. Eg. given a set {1, 4, 6, 7} and x = 10 the answer is yes because {4, 6} sums to 10. Remember that the subsequence need not to be contiguous. For instance if x = 8 in above example the answer is still yes because {1, 7} sums to 8.

- The word knapsack can mean: a backpack the knapsack problem a math problem the subset sum problem a special case of the above Naccache - Stern knapsack
- assess which Xj has no relationship with y at all, and to identify which subsets of the Xj contain redundant information about y. Linear regression models

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