Article
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This version is not peer-reviewed
Solving NP-Complete Problems Efficiently
Version 1
: Received: 22 August 2024 / Approved: 22 August 2024 / Online: 22 August 2024 (11:00:00 CEST)
How to cite: Vega, F. Solving NP-Complete Problems Efficiently. Preprints 2024, 2024081631. https://doi.org/10.20944/preprints202408.1631.v1 Vega, F. Solving NP-Complete Problems Efficiently. Preprints 2024, 2024081631. https://doi.org/10.20944/preprints202408.1631.v1
Abstract
The P versus NP problem is a fundamental question in computer science. It asks whether problems whose solutions can be quickly verified can also be quickly solved. Here, "quickly" refers to computational time that grows proportionally to the size of the input (polynomial time). While the problem's roots trace back to a 1955 letter from John Nash, its formalization is attributed to Stephen Cook and Leonid Levin. Despite extensive research, a definitive answer remains elusive. Closely tied to this is the concept of NP-completeness. If a single NP-complete problem could be solved efficiently, it would imply that all problems in NP can be solved efficiently, proving that P equals NP. This work posits that ONE-IN-THREE 3SAT, a notoriously difficult NP-complete problem, can be solved efficiently, thereby establishing the equivalence of P and NP.
Keywords
Complexity classes; Graph; Polynomial time; Boolean formula
Subject
Computer Science and Mathematics, Data Structures, Algorithms and Complexity
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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