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

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...

knapsack problem is often used to refer specifically to the subset sum problem. The subset sum problem is one of Karp's 21 NP-complete problems. Knapsack...

{\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...

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...

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

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...

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...

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)...

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...

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...

{\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...

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

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...

numbers N {\displaystyle \mathbb {N} } is a subset of Z {\displaystyle \mathbb {Z} } , which in turn is a subset of the set of all rational numbers Q {\displaystyle...

In mathematics, the infimum (abbreviated inf; pl.: infima) of a subset S {\displaystyle S} of a partially ordered set P {\displaystyle P} is the greatest...

\right\|={\sqrt {\sum _{j=1}^{L}(p(j)-m_{i}(j))^{2}}}} . Due to the stochastic nature of context, it is almost never the case in multiple trace theory that...

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...

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...

function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and...

{\sum _{F\subset A\cap B}\left|\int {\mathcal {D}}\varphi O_{\text{in}}[\varphi ]e^{i{\mathcal {S}}[\varphi ]}F[\varphi ]\right|^{2}}{\sum _{F\subset A}\left|\int...

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...

; Koksalan, M. (2009). "Generating a Representative Subset of the Efficient Frontier in Multiple Criteria Decision Making". Operations Research. 57: 187–199...

the sum of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of those divisors sums to...

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}}...

mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as...