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Provided the floating-point arithmetic is correctly rounded to nearest (with ties resolved any way), as is the default in IEEE 754, and provided the sum does not overflow and, if it underflows, underflows gradually, it can be proven that + = +. [1] [6] [2]
The subset sum problem is a special case of the decision and 0-1 problems where each kind of item, the weight equals the value: =. In the field of cryptography, the term 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. [2]
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 ]
In the guillotine cutting problem, both the items and the "bins" are two-dimensional rectangles rather than one-dimensional numbers, and the items have to be cut from the bin using end-to-end cuts. In the selfish bin packing problem, each item is a player who wants to minimize its cost. [53]
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.
It becomes easier to solve with less calculations required. A reasonable value for u could be u = t·t/4 for the corresponding t based on the largest product of two factors whose sum are t being (t/2)·(t/2). Now the problem has a unique solution in the ranges 47 < t < 60, 71 < t < 80, 107 < t < 128, and 131 < t < 144 and no solution below that ...
The assignment problem consists of finding, in a weighted bipartite graph, a matching of maximum size, in which the sum of weights of the edges is minimum. If the numbers of agents and tasks are equal, then the problem is called balanced assignment, and the graph-theoretic version is called minimum-cost perfect matching.
The maximum clique problem is the special case in which all weights are equal. [15] As well as the problem of optimizing the sum of weights, other more complicated bicriterion optimization problems have also been studied. [16] In the maximal clique listing problem, the input is an undirected graph, and the output is a list of all its maximal ...