Polynomial solvability of NP-complete problems

Panyukov, Anatoly V.

doi:10.14293/s2199-1006.1.sor-compsci.ab0dlx.v1

ScienceOpen Research

2014

DOI: 10.14293/s2199-1006.1.sor-compsci.ab0dlx.v1

|View full text |Cite

Polynomial solvability of NP-complete problems

Anatoly V. Panyukov¹

Abstract: A polynomial algorithm for solving the "Hamiltonian circuit" problem is presented in the paper. Computational complexity of the algorithm is equal to Oðn 8 log 2 2 nÞ, where n is the cardinality of the observed graph vertex set. Thus, the polynomial solvability for N P-complete problems is proved.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Computer-Aided Verification of P/NP Proofs: A Survey and Discussion

Rass,

Jakobitsch,

Haan

et al. 2024

IEEE Access

View full text Add to dashboard Cite

We survey a collection of proofs towards equality, inequality or independence of the relation of P to NP. Since the problem has attracted much attention from experts, amateurs and in-betweens, this work is intended as a pointer into directions to enable a ''self-assessment'' of ideas laid out by people interested in the problem. To this end, we identify the most popular approaches to proving equality, inequality or independence. Since the latter category appears to be without any attempts following the necessary proof strategies, we devote a section to an intuitive outline of how independence proofs would work. In the other cases of proving equality or inequality, known barriers like (affine) relativization, algebrization and others are to be avoided. The most important and powerful technique available in this regard is formalization of arguments in automated proof assistants. This allows an objective self-check of a proof before presenting it to the scientific community.

show abstract

Computer-Aided Verification of P/NP Proofs: A Survey and Discussion

Rass,

Jakobitsch,

Haan

et al. 2024

IEEE Access

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Polynomial solvability of NP-complete problems

Cited by 1 publication

References 9 publications

Computer-Aided Verification of P/NP Proofs: A Survey and Discussion

Computer-Aided Verification of P/NP Proofs: A Survey and Discussion

Contact Info

Product

Resources

About