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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 additive combinatorics, the sumset (also called the Minkowski sum) of two subsets and of an abelian group (written additively) is defined to be the set of all sums of an element from with an element from .
The most naïve algorithm would be to cycle through all subsets of n numbers and, for every one of them, check if the subset sums to the right number. The running time is of order O ( 2 n ⋅ n ) {\displaystyle O(2^{n}\cdot n)} , since there are 2 n {\displaystyle 2^{n}} subsets and, to check each subset, we need to sum at most n elements.
Count-subset-sum (#SubsetSum) - finding the number of distinct subsets with a sum of at most C. [25] Restricted shortest path: finding a minimum-cost path between two nodes in a graph, subject to a delay constraint. [26] Shortest paths and non-linear objectives. [27] Counting edge-covers. [28] Vector subset search problem where the dimension is ...
) to sum up a subrectangle of its values; each coloured spot highlights the sum inside the rectangle of that colour. A summed-area table is a data structure and algorithm for quickly and efficiently generating the sum of values in a rectangular subset of a grid.
where A is a finite nonempty subset of a field F, and p(F) is a prime p if F is of characteristic p, and p(F) = ∞ if F is of characteristic 0. Various extensions of this result were given by Noga Alon , M. B. Nathanson and I. Ruzsa in 1996, [ 11 ] Q. H. Hou and Zhi-Wei Sun in 2002, [ 12 ] and G. Karolyi in 2004.
The board B is any subset of the squares of a rectangular board with n rows and m columns; we think of it as the squares in which one is allowed to put a rook. The coefficient , r k ( B ) of x k in the rook polynomial R B ( x ) is the number of ways k rooks, none of which attacks another, can be arranged in the squares of B .
The notion is a generalization of concepts such as subsets from set theory, subgroups from group theory, [1] and subspaces from topology. Since the detailed structure of objects is immaterial in category theory, the definition of subobject relies on a morphism that describes how one object sits inside another, rather than relying on the use of ...