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Partition problem

In number theory and computer science, the partition problem, or number partitioning, is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S1 and S2 such that the sum of the numbers in S1 equals the sum of the numbers in S2. Although the partition problem is NP-complete, there is a pseudo-polynomial…

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Approximation algorithms

Exact algorithms

Hard instances and phase-transition

Probabilistic version

Variants and generalizations

Applications

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Partition problem

Nodes47
Edges46
Triples55
Avg. degree1.96
Density0.042553
Components1

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Partition problem

Top relations

related to Exact algorithms · 18
Partition problem → Algorithms, CGA, CKK, Each, In, It, Its, Karp, KK, NP-hard, Since, Some, The, The Complete Greedy Algorithm, The Complete Karmarkar, There, This, Traversing
related to Approximation algorithms · 15
Partition problem → Algorithms, As, FPTAS, Greedy, However, If, In, It, Karmarkar, Karp, Largest Differencing Method, Sorting, The, Therefore, Theta
related to Computational hardness · 7
Partition problem → An, Given, NP, Partition, SubsetSum, The, This
related to Examples · 7
Partition problem → An, Both, Given, Not, S1, S2, This
has application · 5
Partition problem → CKK, If, One, Suppose, The
is a · 3
Partition problem → special case of multiway-partitioning and of subset-sum, special case of two related problems, two sets S1

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Important terminology

partition problem sum number solution partitioning algorithm time set numbers case two subsets instance subset approximation algorithms input given elements

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Partition problemis aspecial case of two related problems0.90text
Partition problemis atwo sets S10.90text
Partition problemis aspecial case of multiway-partitioning and of subset-sum0.90text
Partition problemhas applicationOne0.60section
Partition problemhas applicationSuppose0.60section
Partition problemhas applicationIf0.60section
Partition problemhas applicationCKK0.60section
Partition problemhas applicationThe0.60section
Partition problemrelated to Approximation algorithmsAs0.60section
Partition problemrelated to Approximation algorithmsTherefore0.60section
Partition problemrelated to Approximation algorithmsAlgorithms0.60section
Partition problemrelated to Approximation algorithmsGreedy0.60section

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