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Subset sum problem

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} . The problem is known to be NP-complete. Moreover, some…

Science, Exponential time algorithms & Computational hardness

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Exponential time algorithms

Naïve algorithmDepth-first searchBinary treeHorowitzSahni
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Computational hardness

Time complexityExhaustive searchDynamic programmingExponential3SAT
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Pseudo-polynomial time dynamic programming solutions

Pseudo-polynomial timeSearch algorithmBFSBacktrackingSIMD
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Polynomial time approximation algorithms

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Computational hardness

Exponential time algorithms

Pseudo-polynomial time dynamic programming solutions

Polynomial time approximation algorithms

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Subset sum problem

Nodes40
Edges39
Triples49
Avg. degree1.95
Density0.05
Components1

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Subset sum problem

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related to Further reading · 41
Subset sum problem → A3, ACM, Algorithms, Charles, Clifford, Computers, Cormen, David, Freeman, Garey, Guide, Intractability, Introduction, ISBN, ISSN, Johnson, Journal, Knapsack, Lagarias, Leiserson
see also · 8
Subset sum problem → Form, Hellman, Knapsack, Mathematical, Multiple, Problem, SSP, The

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Important terminology

displaystyle sum subset algorithm problem ssp time integers number positive input two given inputs instance elements sums exactly variant also

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SubjectPredicateObjectConfidenceSrc
Subset sum problemrelated to Further readingCormen0.60section
Subset sum problemrelated to Further readingThomas0.60section
Subset sum problemrelated to Further readingLeiserson0.60section
Subset sum problemrelated to Further readingCharles0.60section
Subset sum problemrelated to Further readingRivest0.60section
Subset sum problemrelated to Further readingRonald0.60section
Subset sum problemrelated to Further readingStein0.60section
Subset sum problemrelated to Further readingClifford0.60section
Subset sum problemrelated to Further readingThe0.60section
Subset sum problemrelated to Further readingIntroduction0.60section
Subset sum problemrelated to Further readingAlgorithms0.60section
Subset sum problemrelated to Further readingMIT Press0.60section

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