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Solution of the Linear Ordering Problem (NP=P)
[article]

2003
*
arXiv
*
pre-print

A polynomial algorithm is obtained for

arXiv:cs/0303008v1
fatcat:fjccbg26rfelra6gfy7jkv47eu
*the**NP*-complete*linear**ordering**problem*. ...*Solution**of**the**Linear**Ordering**Problem*(*NP*=*P*) G. ... We denote*the*corresponding polytope by B n .*The*polytope B n has integer vertices corresponding to feasible*solutions**of**the**linear**ordering**problem*as well as non-integer vertices. ...##
###
P = NP
[article]

2017
*
arXiv
*
pre-print

*The*present work proves that

*P*=

*NP*. ... In more detail, machine M_AcceptingPath uses a reduction

*of*

*the*initial string

*problem*to another string

*problem*TCPE (defined in

*the*paper) that is

*NP*-complete and decidable in polynomial time. ...

*The*shortened formulation

*of*

*the*

*problem*is

*P*=?

*NP*.

*The*papers [5] [6] [7] [8] [9] contain detailed surveys on

*the*

*P*vs.

*NP*

*Problem*.

*The*present paper proves that

*P*=

*NP*. ...

##
###
P=NP
[article]

2004
*
arXiv
*
pre-print

We claim to resolve

arXiv:cs/0406056v1
fatcat:n6ova5i6ubezpgmlkhv7ceiity
*the**P*=?*NP**problem*via a formal argument for*P*=*NP*. ... Building*the*structure and*the**solution*(and*the*container for*the**solution*) requires steps*linear*in*the*size*of*n, and dipping and withdrawing make two steps, so despite*the*fact that STP is*NP*-complete ...*of**the*1000 or so currently catalogued*NP*-complete*problems*. ...##
###
P versus NP on NP-completeness

2017
*
Figshare
*

*P*versus

*NP*is considered as one

*of*

*the*most important open

*problems*in computer science. This consists in knowing

*the*answer

*of*

*the*following question: Is

*P*equal to

*NP*? ... To attack

*the*

*P*versus

*NP*question

*the*concept

*of*

*NP*-completeness has been very useful. We prove some interesting results regarding this class which affect directly to

*the*

*P*versus

*NP*

*problem*. ... On

*the*other hand,

*the*OTHER-L is a

*problem*

*of*deciding given a

*solution*y

*of*an instance x in a language L whether x has another

*solution*different

*of*y. ...

##
###
P vs. NP
[article]

2016
*
arXiv
*
pre-print

Finally,

arXiv:1601.03619v1
fatcat:vqp6fy5pgbaojea4l2ssuck5e4
*the*lower bound*of*such decision trees is demonstrated to not be in*P*. ... This method is then extended to optimal algorithms which may find all cliques*of*size q in network N, or simply*the*first clique*of*size q in network N. ... Informal Definition*of**NP*-complete Informally, we may refer to*NP*-complete as*the*set*of**problems*which are in*NP*but are possibly not in*P*. ...##
###
P Versus Np

2018
*
Zenodo
*

*P*versus

*NP*is considered as one

*of*

*the*most important open

*problems*in computer science. This consists in knowing

*the*answer

*of*

*the*following question: Is

*P*equal to

*NP*? ... Moreover, we demonstrate this

*problem*is

*NP*-complete. To attack

*the*

*P*versus

*NP*question

*the*concept

*of*

*NP*-completeness has been very useful. ... Certainly,

*P*versus N

*P*is one

*of*

*the*greatest open

*problems*in science and a correct

*solution*for this incognita will have a great impact not only for computer science, but for many other fields as well ...

##
###
Philosophical Solution to P=?NP: P is Equal to NP
[article]

2016
*
arXiv
*
pre-print

*The*

*P*=?

*NP*

*problem*is philosophically solved by showing

*P*is equal to

*NP*in

*the*random access with unit multiply (MRAM) model. ... Since

*the*computation power

*of*MRAMs is

*the*same as NDTMs,

*P*is equal to

*NP*.

*The*paper shows that

*the*justification for

*the*NDTM

*P*? ...

*The*paper also defends Deolaliker'ss cientific

*solution*to

*the*

*P*=?

*NP*

*problem*where he shows

*P*not equal to

*NP*using properties

*of*

*the*statistical physics

*of*Boltzmann gases. ...

##
###
P versus NP

2020
*
Zenodo
*

*P*versus

*NP*is considered as one

*of*

*the*most important open

*problems*in computer science. This consists in knowing

*the*answer

*of*

*the*following question: Is

*P*equal to

*NP*? ... However, a precise statement

*of*

*the*

*P*versus

*NP*

*problem*was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this

*problem*have failed. ... We show some results that prove this outstanding

*problem*with

*the*unexpected

*solution*

*of*

*P*= N

*P*. 2 Theory and Methods Preliminaries In 1936, Turing developed his theoretical computational model ...

##
###
P versus NP

2020
*
Zenodo
*

*P*versus

*NP*is considered as one

*of*

*the*most important open

*problems*in computer science. This consists in knowing

*the*answer

*of*

*the*following question: Is

*P*equal to

*NP*? ... However, a precise statement

*of*

*the*

*P*versus

*NP*

*problem*was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this

*problem*have failed. ... We show some results that prove this outstanding

*problem*with

*the*unexpected

*solution*

*of*

*P*= N

*P*. 2 Theory and Methods Preliminaries In 1936, Turing developed his theoretical computational model ...

##
###
P versus NP

2020
*
Zenodo
*

*P*versus

*NP*is considered as one

*of*

*the*most important open

*problems*in computer science. This consists in knowing

*the*answer

*of*

*the*following question: Is

*P*equal to

*NP*? ... However, a precise statement

*of*

*the*

*P*versus

*NP*

*problem*was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this

*problem*have failed. ... We show some results that prove this outstanding

*problem*with

*the*unexpected

*solution*

*of*

*P*= N

*P*. 2 Theory and Methods Preliminaries In 1936, Turing developed his theoretical computational model ...

##
###
P versus NP

2020
*
Zenodo
*

*P*versus

*NP*is considered as one

*of*

*the*most important open

*problems*in computer science. This consists in knowing

*the*answer

*of*

*the*following question: Is

*P*equal to

*NP*? ... However, a precise statement

*of*

*the*

*P*versus

*NP*

*problem*was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this

*problem*have failed. ... We show some results that prove this outstanding

*problem*with

*the*unexpected

*solution*

*of*

*P*= N

*P*. 2 Theory and Methods Preliminaries In 1936, Turing developed his theoretical computational model ...

##
###
A note on xQx as a modelling and solution framework for the Linear Ordering Problem

2009
*
International Journal of Operational Research
*

In this paper, we demonstrate that

doi:10.1504/ijor.2009.025005
fatcat:wxp55mah6be6zbdqds3joiwb3u
*the**Linear**Ordering**Problem*(LOP) can be easily recast so that it can be treated as a UQP*problem*, and that large instances*of**the*LOP can be effectively handled within ... This paper expands*the*list*of*0-1*problems*that can be effectively modelled and solved as Unconstrained Quadratic Binary Programs (UQPs). ... Acknowledgement We thank*the*anonymous reviewers for their careful attention to detail and helpful comments. ...##
###
P versus NP

2019
*
Zenodo
*

*P*versus

*NP*is considered as one

*of*

*the*most important open

*problems*in computer science. This consists in knowing

*the*answer

*of*

*the*following question: Is

*P*equal to

*NP*? ... A precise statement

*of*

*the*

*P*versus

*NP*

*problem*was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this

*problem*have failed. ... We show some results that prove this outstanding

*problem*with

*the*unexpected

*solution*

*of*

*P*= N

*P*. 2 Theory and Methods Preliminaries In 1936, Turing developed his theoretical computational model ...

##
###
P versus NP

2019
*
Zenodo
*

*P*versus

*NP*is considered as one

*of*

*the*most important open

*problems*in computer science. This consists in knowing

*the*answer

*of*

*the*following question: Is

*P*equal to

*NP*? ... A precise statement

*of*

*the*

*P*versus

*NP*

*problem*was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this

*problem*have failed. ...

*The*following consequences are assuming that we have a practical

*solution*for

*the*

*NP*-complete

*problems*where such existence was proven with our nonconstructive result: 1. ...

##
###
P versus NP

2019
*
Zenodo
*

*P*versus

*NP*is considered as one

*of*

*the*most important open

*problems*in computer science. This consists in knowing

*the*answer

*of*

*the*following question: Is

*P*equal to

*NP*? ... A precise statement

*of*

*the*

*P*versus

*NP*

*problem*was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this

*problem*have failed. ...

*The*following consequences are assuming that we have a practical

*solution*for

*the*

*NP*-complete

*problems*where such existence was proven with our nonconstructive result: 1. ...

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