Search results
Results from the WOW.Com Content Network
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 ...
In computer science, greedy number partitioning is a class of greedy algorithms for multiway number partitioning. The input to the algorithm is a set S of numbers, and a parameter k. The required output is a partition of S into k subsets, such that the sums in the subsets are as nearly equal as possible. Greedy algorithms process the numbers ...
[1]: sec.5 The problem is parametrized by a positive integer k, and called k-way number partitioning. [2] The input to the problem is a multiset S of numbers (usually integers), whose sum is k*T. The associated decision problem is to decide whether S can be partitioned into k subsets such that the sum of each subset is exactly T.
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.
Another special case called 3-partitioning is when the number of items in each subset should be at most 3 (k = 3). Deciding whether there exists such a partition with equal sums is exactly the 3-partition problem, which is known to be strongly NP-hard. There are approximation algorithms that aim to find a partition in which the sum is as nearly ...
In computer science, pseudopolynomial time number partitioning is a pseudopolynomial time algorithm for solving the partition problem.. The problem can be solved using dynamic programming when the size of the set and the size of the sum of the integers in the set are not too big to render the storage requirements infeasible.
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 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 ...
In 3-Partition the goal is to partition S into m = n/3 subsets, not just a fixed number of subsets, with equal sum. Partition is "easier" than 3-Partition: while 3-Partition is strongly NP-hard, Partition is only weakly NP-hard - it is hard only when the numbers are encoded in non-unary system, and have value exponential in n.