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 partition problem is a special case of two related problems: In the subset sum problem, the goal is to find a subset of S whose sum is a certain target...

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...

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

key for decryption. It is based on the subset sum problem (a special case of the knapsack problem). The problem is as follows: given a set of integers...

polynomial-time algorithms for NP-hard problems exist. A simple example of an NP-hard problem is the subset sum problem. Informally, if H is NP-hard, then...

maximum sum subarray problem, also known as the maximum segment sum problem, is the task of finding a contiguous subarray with the largest sum, within...

by David J. Grynkiewicz in 2005). Barycentric-sum problem Davenport constant Subset sum problem Zero-sum Ramsey theory Erdős, Paul; Ginzburg, A.; Ziv,...

spacePages displaying short descriptions of redirect targets Subset sum problem – Decision problem in computer science Subsumptive containment – System of...

subset sum problem can be reduced to the problem of computing the required partition C1, C2, ..., Cn of columns: Given an input set S for the subset sum...

given subset has sum zero is a verifier. Clearly, summing the integers of a subset can be done in polynomial time, and the subset sum problem is therefore...

theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural...

collection, referred to as S, of a given m subsets whose union equals the universe, the set cover problem is to identify a smallest sub-collection of...

For example, an early suggestion was to use schemes based on the subset sum problem. This turned out rather quickly to be unsuitable. As of 2004[update]...

Partition problem: SP12  Quadratic assignment problem: ND43  Quadratic programming (NP-hard in some cases, P if convex) Subset sum problem: SP13  Variations...

no such subset). This optimization problem is similar to the decision problem SUBSET-SUM. Given a set of integers, SUBSET-SUM is the problem of finding...

tours, each visiting only a subset of the vertices; arguably, it is this global requirement that makes TSP a hard problem. The MTZ and DFJ formulations...

fibered sum in category theory QCD sum rules, in quantum field theory Riemann sum, in calculus Rule of sum, in combinatorics Subset sum problem, in cryptography...

problem attacked in this way was the Hamiltonian path problem. The simplest one is the subset sum problem. An optical device solving an instance with four...

known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem. Its solution is also...

on calculations involving the subset sum problem) to show that every integer greater than 96 may be represented as a sum of distinct super-prime numbers...

partitioning is the problem of partitioning a multiset of numbers into a fixed number of subsets, such that the sums of the subsets are as similar as possible...

weakly NP-complete problem is the subset sum problem. The related term strongly NP-complete (or unary NP-complete) refers to those problems that remain NP-complete...

designed such that the problem of finding collisions should be reducible to a known and hard mathematical problem (the subset sum problem). It means that if...

isomorphism problem Subset sum problem Clique problem Vertex cover problem Independent set problem Dominating set problem Graph coloring problem Sudoku To...

Finding such a cut is known as the max-cut problem. The problem can be stated simply as follows. One wants a subset S of the vertex set such that the number...

a_{n-1})\mid \sum _{i=0}^{n-1}a_{i}x^{i}\in I\right\}\subset \mathbb {Z} ^{n}.} Theorem: L ⊂ Z n {\displaystyle {\mathfrak {L}}\subset \mathbb {Z} ^{n}}...

A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all...

solve SUBSET-SUM in polynomial time is b bits long, the above algorithm will try at least 2b − 1 other programs first. A decision problem is a problem that...

knapsack problem: If for each item the profit and weight are equal, we get the subset sum problem (often the corresponding decision problem is given instead):...