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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 and a target-sum T {\displaystyle T} , and the question is to decide whether any subset of the integers sum to precisely T {\displaystyle T} . [ 1 ]
It is a generalization of the subset sum problem. The input to the problem is a multiset of n integers and a positive integer m representing the number of subsets. The goal is to construct, from the input integers, some m subsets. The problem has several variants: Max-sum MSSP: for each subset j in 1,...,m, there is a capacity C j.
Catch best algorithm solve subset sum problem O(N*2^(N/2)). Proof: million dollar solution solve NP-complete problem, circuit optimize. Proof NP-complete problem hard. Cryptograph algorithm base NP-complete problem. Solve algorithm worth< cryptography. Describe solution subset sum problem. Simple algorithm solve subset sum problem.
In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem.On input a formula over Boolean variables, such as "(x or y) and (x or not y)", a SAT solver outputs whether the formula is satisfiable, meaning that there are possible values of x and y which make the formula true, or unsatisfiable, meaning that there are no such ...
The partition problem - a special case of multiway number partitioning in which the number of subsets is 2. The 3-partition problem - a different and harder problem, in which the number of subsets is not considered a fixed parameter, but is determined by the input (the number of sets is the number of integers divided by 3).
A is a subset of B (denoted ) and, conversely, B is a superset of A (denoted ). In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B.
An evaluation of the variables is a function from a subset of variables to a particular set of values in the corresponding subset of domains. An evaluation v {\displaystyle v} satisfies a constraint t j , R j {\displaystyle \langle t_{j},R_{j}\rangle } if the values assigned to the variables t j {\displaystyle t_{j}} satisfy the relation R j ...
Given a set of elements {1, 2, …, n} (henceforth referred to as the universe, specifying all possible elements under consideration) and a 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 S whose union equals the universe.