The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers...

The multiple subset sum problem is an optimization problem in computer science and operations research. It is a generalization of the subset sum problem...

subset sum problem. The subset sum problem is one of Karp's 21 NP-complete problems. A generalization of subset sum problem is called multiple subset-sum...

each class, we get the multiple-choice knapsack problem: If for each item the profit and weight are equal, we get the subset sum problem (often the corresponding...

says that any multiset of 2n − 1 integers has a subset of size n the sum of whose elements is a multiple of n, but that the same is not true of multisets...

finite subset A 0 {\displaystyle A_{0}} of I {\displaystyle I} such that S − ∑ i ∈ A a i ∈ V  for every finite superset A ⊇ A 0 . {\displaystyle S-\sum _{i\in...

interpretation: the left side sums the number of subsets of {1, ..., n} of sizes k = 0, 1, ..., n, giving the total number of subsets. (That is, the left side...

In machine learning, feature selection is the process of selecting a subset of relevant features (variables, predictors) for use in model construction...

considers a set of statistical inferences simultaneously or estimates a subset of parameters selected based on the observed values. The larger the number...

{\displaystyle 1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+{\frac {1}{5}}+\cdots =\sum _{n=1}^{\infty }{\frac {1}{n}}.} The divergence of the harmonic series was...

variance of Y. The expression above can be extended to a weighted sum of multiple variables: Var ⁡ ( ∑ i n a i X i ) = ∑ i = 1 n a i 2 Var ⁡ ( X i )...

least squares computes the unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane)...

for the two-dimensional knapsack problem. The same is true for the multiple subset sum problem: the quasi-dominance relation should be: s quasi-dominates...

subset of powers of 2, which does not have any upper bound. If the number 0 is included, this will be the greatest element, since this is a multiple of...

{\displaystyle \sum _{b\in B}\left|x(b)\right|^{2}=\sup \sum _{n=1}^{N}\left|x(b_{n})\right|^{2}} the supremum being taken over all finite subsets of B. It follows...

partitioning a multiset of numbers into a fixed number of subsets, such that the sums of the subsets are as similar as possible. It was first presented by...

a finite subset of A, one can replace the unweighted cardinality |B| of B by the weighted cardinality ∑ a ∈ B w ( a ) . {\displaystyle \sum _{a\in B}w(a)...

Zermelo–Fraenkel set theory, the axiom of choice entails that non-measurable subsets of R {\displaystyle \mathbb {R} } exist. The notion of a non-measurable...

all finite subsets of A {\displaystyle A} directed by inclusion ⊆ {\displaystyle \subseteq } and x H := ∑ i ∈ H x i {\textstyle x_{H}:=\sum _{i\in H}x_{i}}...

infinite series formed by summing all positive unit fractions: ∑ n = 1 ∞ 1 n = 1 + 1 2 + 1 3 + 1 4 + 1 5 + ⋯ . {\displaystyle \sum _{n=1}^{\infty }{\frac...

different definitions are common. 1.   A ⊂ B {\displaystyle A\subset B} may mean that A is a subset of B, and is possibly equal to B; that is, every element...

algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called...

no linear relationship with the response at all, or to identify which subsets of explanatory variables may contain redundant information about the response...

ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and...

compact subset K of U intersects the support of only finitely many g p , {\displaystyle g_{p},} and T = ∑ p ∂ p g p . {\displaystyle T=\sum \nolimits...

{\displaystyle \sum _{i=1}^{m}k_{i}=n} . The coefficient above counts the number of flags V 1 ⊂ ⋯ ⊂ V m {\displaystyle V_{1}\subset \dots \subset V_{m}} of...

phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome...

in X . {\displaystyle X.} The sum of a compact set and a closed set is closed. However, the sum of two closed subsets may fail to be closed (see this...

to the theorem, it is possible to expand the polynomial (x + y)n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative...

They can also be finite, countably infinite, or uncountably infinite. A subset of the sample space is an event, denoted by E {\displaystyle E} . If the...