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Max-sum MSSP: for each subset j in 1,...,m, there is a capacity C j. The goal is to make the sum of all subsets as large as possible, such that the sum in each subset j is at most C j. [1] Max-min MSSP (also called bottleneck MSSP or BMSSP): again each subset has a capacity, but now the goal is to make the smallest subset sum as large as ...
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely . [1] The problem is known to be NP-complete.
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 .
Given a family (repeats allowed) of subsets A 1, A 2, ..., A n of a universal set S, the principle of inclusion–exclusion calculates the number of elements of S in none of these subsets. A generalization of this concept would calculate the number of elements of S which appear in exactly some fixed m of these sets.
) 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.
Given a set of integers, SUBSET-SUM is the problem of finding whether there exists a subset summing to zero. SUBSET-SUM is NP-complete. To show that FIND-SUBSET-SUM is NP-equivalent, we must show that it is both NP-hard and NP-easy. Clearly it is NP-hard. If we had a black box that solved FIND-SUBSET-SUM in unit time, then it would be easy to ...
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 ...
For K and L compact convex subsets in , the Minkowski sum can be described by the support function of the convex sets: + = +. For p ≥ 1, Firey [11] defined the L p Minkowski sum K + p L of compact convex sets K and L in containing the origin as