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NP-Complete decision problems for binary quadratics

Kenneth L. Manders, Leonard Adleman
1978 Journal of computer and system sciences (Print)  
Thus only the question 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] .  ... 
doi:10.1016/0022-0000(78)90044-2 fatcat:bmhpbziwwvbgpgcslr66jv3pua

Computational Complexity of Quadratic Unconstrained Binary Optimization [article]

Hirotoshi Yasuoka
2022 arXiv   pre-print
In this paper, we study the computational complexity of the 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.  ... 
arXiv:2109.10048v2 fatcat:pmovoz3y3jft7j42glozpcvgzm

MPF Problem over Modified Medial Semigroup Is NP-Complete

Eligijus Sakalauskas, Aleksejus Mihalkovich
2018 Symmetry  
We are considering a 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.  ... 
doi:10.3390/sym10110571 fatcat:sr7lkoc3bbennip4vdnzxx37au

NP-complete decision problems for quadratic polynomials

Kenneth Manders, Leonard Adleman
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 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  ... 
doi:10.1145/800113.803627 dblp:conf/stoc/MandersA76 fatcat:sim4pz2f6ndkvmrc6vx66uur7a

Mixed-integer Quadratic Programming is in NP [article]

Alberto Del Pia, Santanu S. Dey, Marco Molinaro
2014 arXiv   pre-print
In this paper, we prove that the 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  ... 
arXiv:1407.4798v1 fatcat:4lv3hbvggrgkvbh4zptj6ywdyy

Mixed-integer quadratic programming is in NP

Alberto Del Pia, Santanu S. Dey, Marco Molinaro
2016 Mathematical programming  
In this paper, we prove that the 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  ... 
doi:10.1007/s10107-016-1036-0 fatcat:kejohfagyjau7g4jidcmlpytdy

The Complexity of Decision Versus Search

Mihir Bellare, Shafi Goldwasser
1994 SIAM journal on computing (Print)  
A basic question about 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  ... 
doi:10.1137/s0097539792228289 fatcat:5h53wc3gsbeqjaneurwasrqa5a

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.  ... 

Binary Solutions for Overdetermined Systems of Linear Equations [article]

Subhendu Das
2011 arXiv   pre-print
This paper presents a finite step method 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.  ... 
arXiv:1101.3056v1 fatcat:gozz6bkaing6jcwk55y2wexg54

Quasilinear time complexity theory [chapter]

Ashish V. Naik, Kenneth W. Regan, D. Sivakumar
1994 Lecture Notes in Computer Science  
We show, however, that the important equivalence between search 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.  ... 
doi:10.1007/3-540-57785-8_134 fatcat:aixgp5vqpfc2li3bvmyfd7f7iq

Petri Net Modeling for Ising Model Formulation in Quantum Annealing

Morikazu Nakamura, Kohei Kaneshima, Takeo Yoshida
2021 Applied Sciences  
models, and then converted into 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.  ... 
doi:10.3390/app11167574 fatcat:2djprequajdpnpah6pmg45jurq

On the theory of average case complexity

Shai Ben-David, Benny Chor, Oded Goldreich, Michel Luby
1992 Journal of computer and system sciences (Print)  
Levin's work can be viewed as the basic 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.  ... 
doi:10.1016/0022-0000(92)90019-f fatcat:ngf4z4bn65binajjhc2zkwabd4

On quasilinear-time complexity theory

Ashish V. Naik, Kenneth W. Regan, D. Sivakumar
1995 Theoretical Computer Science  
We show, however, that the important equivalence between search 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.  ... 
doi:10.1016/0304-3975(95)00031-q fatcat:rjdzekyykfcajflu7tylnlkaf4

On the theory of average case complexity

S. Ben-David, B. Chor, O. Goldreich
1989 Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89  
Our results include: the equivalence of search and 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.  ... 
doi:10.1145/73007.73027 dblp:conf/stoc/Ben-DavidCGL89 fatcat:3hmaanxtzjcwjbm4bxjxmysrcq

Formulations for joint order picking problems in low-level picker-to-part systems

Jose Alejandro Cano
2020 Bulletin of Electrical Engineering and Informatics  
The number of constraints and 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  ... 
doi:10.11591/eei.v9i2.2110 fatcat:ptglqblwvnc7fevfkubc7p4nxa
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