Graph-Based Deterministic Polynomial Algorithm for NP Problems Article Swipe
The P vs NP problem asks whether every problem whose solution can be verified in polynomialtime (NP) can also be solved in polynomial time (P). In this paper, we present a proof that P =NP, demonstrating that every NP problem can be solved deterministically in polynomial time usinga graph-based algorithm. We introduce a new Computation Model that enables the simulation ofa Turing machine, and show that NP problems can be simulated efficiently within this framework.By introducing the concept of a Feasible Graph, we ensure that the simulation can be performedin polynomial time, providing a direct path to resolving the P = NP question. Our result hassignificant implications for fields such as cryptography, optimization, and artificial intelligence, whereNP-complete problems play a central role.
Related Topics
Concepts
Time complexity
P versus NP problem
Path (computing)
Polynomial
Algorithm
Mathematics
Computation
Turing machine
Turing
NP-complete
Computer science
Computational complexity theory
NP
Matrix polynomial
Discrete mathematics
Model of computation
Running time
Stable polynomial
Wilkinson's polynomial
Mathematical optimization
Theoretical computer science
Efficient algorithm
Metadata
- Type
- preprint
- Landing Page
- https://doi.org/10.5281/zenodo.17784110
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7108338965
All OpenAlex metadata
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https://openalex.org/W7108338965Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.5281/zenodo.17784110Digital Object Identifier
- Title
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Graph-Based Deterministic Polynomial Algorithm for NP ProblemsWork title
- Type
-
preprintOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
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2025-12-02Full publication date if available
- Authors
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Lee, ChangryeolList of authors in order
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https://doi.org/10.5281/zenodo.17784110Publisher landing page
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://doi.org/10.5281/zenodo.17784110Direct OA link when available
- Concepts
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Time complexity, P versus NP problem, Path (computing), Polynomial, Algorithm, Mathematics, Computation, Turing machine, Turing, NP-complete, Computer science, Computational complexity theory, NP, Matrix polynomial, Discrete mathematics, Model of computation, Running time, Stable polynomial, Wilkinson's polynomial, Mathematical optimization, Theoretical computer science, Efficient algorithmTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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