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NP-Complete decision problems for binary quadratics

1978
*
Journal of computer and system sciences (Print)
*

Thus only the question

doi:10.1016/0022-0000(78)90044-2
fatcat:bmhpbziwwvbgpgcslr66jv3pua
*for**binary**quadratics*remains in the gap between tractable ("xl2 + I% -y = 0, % it Y 65 WY the*problem*of deciding whether there are natural-number solutions is*NP*-*complete*... We show that*for*the two-variable*quadratics*of the form c& + fly -y = 0; 01, fi, y E w, the*problem*is &Y-*complete*. Xl .*a x,J = 0 has a solution). ... OPEN*PROBLEM*7 (classification of the set PY of prime numbers). PY E*NP*[17] , and PY E P(ERH) [15] . ...##
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Computational Complexity of Quadratic Unconstrained Binary Optimization
[article]

2022
*
arXiv
*
pre-print

In this paper, we study the computational complexity of the

arXiv:2109.10048v2
fatcat:pmovoz3y3jft7j42glozpcvgzm
*quadratic*unconstrained*binary*optimization (QUBO)*problem*under the functional*problem*FP^*NP*categorization. ... We also study the computational complexity of the*decision*version of the QUBO*problem*with integer coefficients. We prove that this*problem*is DP-*complete*. ... Acknowledgements We want to thank Akira Miki and Chih-Hong Cheng*for*useful advice. ...##
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MPF Problem over Modified Medial Semigroup Is NP-Complete

2018
*
Symmetry
*

We are considering a

doi:10.3390/sym10110571
fatcat:sr7lkoc3bbennip4vdnzxx37au
*problem*introduced in our previous paper and prove that tis*problem*is*NP*-*Complete*. ... The proof is based on the dual interpretation of well known multivariate*quadratic*(MQ)*problem*defined over the*binary*field as a system of MQ equations, and as a general satisfiability (GSAT)*problem*... Therefore, it is very desirable to try to prove*NP*-*Completeness*of MPF*problem*. In [6] the*NP*-*Completeness*of a more general*problem*named as multivariate*quadratic*power*problem*is presented. ...##
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NP-complete decision problems for quadratic polynomials

1976
*
Proceedings of the eighth annual ACM symposium on Theory of computing - STOC '76
*

In this a r t i c l e we show the

doi:10.1145/800113.803627
dblp:conf/stoc/MandersA76
fatcat:sim4pz2f6ndkvmrc6vx66uur7a
*NP*-*completeness*of some simple number-theoretic*problems*. Natural simplifications of these*problems*invariably are known to be in P. ... Unless P=*NP*this is impossible, even*for*a class of*quadratic*diophantine equations in two unknowns*for*which a*decision*procedure in the original sense is in fact a v a i l a b l e . . ... be*NP*-*complete*, we hope that the*NP*-*completeness*of these*problems*w i l l play a role in showing the*NP*-*completeness*of further*problems*of a numerical nature, much as the s a t i s f i a b i l i t y ...##
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Mixed-integer Quadratic Programming is in NP
[article]

2014
*
arXiv
*
pre-print

In this paper, we prove that the

arXiv:1407.4798v1
fatcat:4lv3hbvggrgkvbh4zptj6ywdyy
*decision*version of mixed-integer*quadratic*programming is in*NP*, thereby showing that it is*NP*-*complete*. ... Mixed-integer*quadratic*programming is the*problem*of optimizing a*quadratic*function over points in a polyhedral set where some of the components are restricted to be integral. ... Corollary 2 . 2 The*decision*versions of IQP and MIQP are*NP*-*complete*. 2 . 2 Two general*quadratic*inequalities: In the presence of two*quadratic*inequalities (in fact one*quadratic*equation) in two ...##
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Mixed-integer quadratic programming is in NP

2016
*
Mathematical programming
*

In this paper, we prove that the

doi:10.1007/s10107-016-1036-0
fatcat:kejohfagyjau7g4jidcmlpytdy
*decision*version of mixed-integer*quadratic*programming is in*NP*, thereby showing that it is*NP*-*complete*. ... Mixed-integer*quadratic*programming (MIQP) is the*problem*of optimizing a*quadratic*function over points in a polyhedral set where some of the components are restricted to be integral. ... Corollary 2 . 2 The*decision*versions of IQP and MIQP are*NP*-*complete*. 2 . 2 Two general*quadratic*inequalities: In the presence of two*quadratic*inequalities (in fact one*quadratic*equation) in two ...##
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The Complexity of Decision Versus Search

1994
*
SIAM journal on computing (Print)
*

A basic question about

doi:10.1137/s0097539792228289
fatcat:5h53wc3gsbeqjaneurwasrqa5a
*NP*is whether or not search reduces in polynomial time to*decision*. ... reduce to*decision*. ... We thank Oded Goldreich*for*many helpful comments on the paper. We thank Satish Thate*for*...##
###
Page 1848 of Mathematical Reviews Vol. , Issue 98C
[page]

1998
*
Mathematical Reviews
*

“We show that a

*binary*algebraic*decision*tree T can be con- verted to a ternary algebraic*decision*tree TJ’ at the expense of a*quadratic*increase in size and a linear increase in depth.” 98c:68068 68Q15 ... there exist*binary**decision*trees*for*which such a simulation necessarily entails an exponential increase in size. ...##
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Binary Solutions for Overdetermined Systems of Linear Equations
[article]

2011
*
arXiv
*
pre-print

This paper presents a finite step method

arXiv:1101.3056v1
fatcat:gozz6bkaing6jcwk55y2wexg54
*for*computing the*binary*solution to an overdetermined system of linear algebraic equations Ax = b, where A is an m x n real matrix of rank n < m, and b is a real ... A class of*binary**quadratic*programming*problem*, such as with non-negative coefficients*for*the*quadratic*terms, is also known as*NP**problem*; see Garey [6, p. 245] . Also see Axehill [1] . ... However, a*problem*very similar to (1) has been defined as*NP*-*complete**problem*by Murty and Kabadi [9] . This*NP*-*complete**problem*is stated as follows. ...##
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Quasilinear time complexity theory
[chapter]

1994
*
Lecture Notes in Computer Science
*

We show, however, that the important equivalence between search

doi:10.1007/3-540-57785-8_134
fatcat:aixgp5vqpfc2li3bvmyfd7f7iq
*problems*and*decision**problems*in polynomial time is unlikely to carry over: if search reduces to*decision**for*SAT in quasi-linear time, ... Whereas all previously known versions of the Valiant-Vazirani reduction from*NP*to parity run in*quadratic*time, we give a new construction using error-correcting codes that runs in quasilinear time. ... We thank Stephen Bloch and Michael Loui*for*comments on earlier versions of this paper, and Jonathan Buss, Judy Goldsmith, Jack Lutz, and Kripa Sundar*for*pertinent discussions. ...##
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Petri Net Modeling for Ising Model Formulation in Quantum Annealing

2021
*
Applied Sciences
*

models, and then converted into

doi:10.3390/app11167574
fatcat:2djprequajdpnpah6pmg45jurq
*binary**quadratic*nets, equivalent to Ising models. ... Quantum annealing is an emerging new platform*for*combinatorial optimization, requiring an Ising model formulation*for*optimization*problems*. ...*For*example, we solve a search variant*decision**problem*to obtain a viable schedule to*complete*all tasks by a given deadline in scheduling*problems*. ...##
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On the theory of average case complexity

1992
*
Journal of computer and system sciences (Print)
*

Levin's work can be viewed as the basic

doi:10.1016/0022-0000(92)90019-f
fatcat:ngf4z4bn65binajjhc2zkwabd4
*for*a theory of average*NP*-*completeness*, much the same way as [2] (and [19]) are the basis*for*the theory of*NP*-*completeness*. ... Our results include: l the equivalence of search and*decision**problems*in the context of average case complexity; 9 an initial analysis of the structure of distributional-*NP*(i.e.,*NP**problems*coupled ... ACKNOWLEDGMENTS We thank Shimon Even, Mauricio Karchmer, Hugo Krawczyk, Ronny Roth, and Avi Wigderson*for*helpful discussions. We are grateful to Leonid Levin*for*very interesting discussions. ...##
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On quasilinear-time complexity theory

1995
*
Theoretical Computer Science
*

We show, however, that the important equivalence between search

doi:10.1016/0304-3975(95)00031-q
fatcat:rjdzekyykfcajflu7tylnlkaf4
*problems*and*decision**problems*in polynomial time is unlikely to carry over: if search reduces to*decision**for*SAT in quasilinear time, then ... Whereas all previously known versions of the Valiant-Vazirani reduction from*NP*to parity run in*quadratic*time, we give a new construction using error-correcting codes that runs in quasilinear time. ... Fischer, Judy Goldsmith, Jack Lutz, and Kripa Sundar*for*pertinent discussions. We also thank the anonymous referees*for*catching a number of technical glitches in our original submission. ...##
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On the theory of average case complexity

1989
*
Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89
*

Our results include: the equivalence of search and

doi:10.1145/73007.73027
dblp:conf/stoc/Ben-DavidCGL89
fatcat:3hmaanxtzjcwjbm4bxjxmysrcq
*decision**problems*in the context of average case complexity; an initial analysis of the structure of distributional-*NP*(i.e. ... Previous works Levin 84, Gurevich 87, Venkatesan and Levin 88] have focused on the existence of*complete**problems*. We widen the scope to other basic questions in computational complexity. ... We are grateful to Leonid Levin*for*very interesting discussions. Finaly, we wish to thank Yuri Gurevich*for*pointing out a misleading statement in an early version of the proof of Theorem 9. ...##
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Formulations for joint order picking problems in low-level picker-to-part systems

2020
*
Bulletin of Electrical Engineering and Informatics
*

The number of constraints and

doi:10.11591/eei.v9i2.2110
fatcat:ptglqblwvnc7fevfkubc7p4nxa
*decision*variables required*for*each proposed model is calculated, demonstrating the complexity of solving medium and long-sized*problems*in reasonable computing time using ... This article introduces several mathematical formulations*for*the joint order picking*problem*(JOPP) in low-level picker-to-part warehousing systems. ... methods prevail as the most suitable option to obtain high -quality solutions in short computing times*for**NP*-Hard*problems*since the*decisions*made at a joint order picking*problem*must be taken repetitively ...
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