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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 ]
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 input to the problem is a multiset S {\displaystyle S} of n integers and a positive integer m representing the number of subsets.
In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S). In multiway number partitioning , there is an integer parameter k , and the goal is to decide whether S can be partitioned into k subsets of equal sum ...
The sum-product conjecture informally says that one of the sum set or the product set of any set must be nearly as large as possible. It was originally conjectured by Erdős in 1974 to hold whether A is a set of integers, reals, or complex numbers. [3] More precisely, it proposes that, for any set A ⊂ ℂ, one has
The problem is rather easily solved once the concepts and perspectives are made clear. There are three parties involved, S, P, and O. S knows the sum X+Y, P knows the product X·Y, and the observer O knows nothing more than the original problem statement. All three parties keep the same information but interpret it differently.
The first is also a perfect matching, while the second is far from it with 4 vertices unaccounted for, but has high value weights compared to the other edges in the graph. In computer science and graph theory , the maximum weight matching problem is the problem of finding, in a weighted graph , a matching in which the sum of weights is maximized.
In this problem, each variable corresponds to an hour that teacher must spend with cohort , the assignment to the variable specifies whether that hour is the first or the second of the teacher's available hours, and there is a 2-satisfiability clause preventing any conflict of either of two types: two cohorts assigned to a teacher at the same ...
In decision theory, the weighted sum model (WSM), [1] [2] also called weighted linear combination (WLC) [3] or simple additive weighting (SAW), [4] is the best known and simplest multi-criteria decision analysis (MCDA) / multi-criteria decision making method for evaluating a number of alternatives in terms of a number of decision criteria.