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A Variable-Complexity Norm Maximization Problem

O. L. Mangasarian, T. -H. Shiau
1986 SIAM Journal on Algebraic and Discrete Methods  
NP is the class of problems solvable by a nondeterministic algorithm in polynomial time, including (4.1) and all other NP-complete problems.  ...  In fact NP-complete problems are the class of most difficult problems in NP in the sense that each problem in NP reduces in polynomial time to each NP-complete problem.  ... 
doi:10.1137/0607052 fatcat:l7gwkdho7vdzfhkmanzzxqy34q

Some Dichotomy Theorems for Neural Learning Problems

Michael Schmitt
2004 Journal of machine learning research  
We determine for each problem class the dividing line between the NP-complete and polynomial-time solvable problems.  ...  The results are established as dichotomy theorems showing that each problem is either NP-complete or solvable in polynomial time.  ...  Acknowledgments I thank the anonymous reviewers for their helpful comments and suggestions.  ... 
dblp:journals/jmlr/Schmitt04 fatcat:bl3cwzg7xbbr7lzgl4qk37edam

Page 183 of Neural Computation Vol. 4, Issue 2 [page]

1992 Neural Computation  
Hopfield and Tank 1985) for solving NP-complete problems would necessarily con- sume exorbitantly large physical resources (Vergis et al. 1986).  ...  There are, however, results that at least make it appear unlikely this problem is NP-complete.  ... 

Polynomial Algorithms for a Class of Discrete Minmax Linear Programming Problems

Abraham P. Punnen, K. P. K. Nair
1995 Journal of the Operational Research Society  
Although this general problem is NP-complete, it is shown that a restricted version of this problem can be solved in polynomial time.  ...  If A and b are arbitrary, then DMLP can easily be shown to be NP-complete.  ... 
doi:10.2307/2584597 fatcat:yzgghw34tbac3ok3baazbupeei

On the inherent intractability of certain coding problems (Corresp.)

E. Berlekamp, R. McEliece, H. van Tilborg
1978 IEEE Transactions on Information Theory  
ACKNOWLEDGMENT We wish to thank one of the referees for pointing out to us the relation between the "weight < w" decision problem and the minimum weight problem for linear codes.  ...  problem of rmding tbe weights of a linear code are both lem, the O-l integer programming problem, and the Hamiltonian NP-complete is shown.  ...  The forthcoming book by Garey and Johnson [3] contains literally hundreds of problems known to be NP-complete; and if the "obvious" assertion NP# P is true then no NP-complete problem can have a polynomial-time  ... 
doi:10.1109/tit.1978.1055873 fatcat:sepkw4wkcndknjvrec2l3z7yyy

Page 4811 of Mathematical Reviews Vol. , Issue 84k [page]

1984 Mathematical Reviews  
trees and matroids; Integer linear programming; A cutting-plane algorithm for integer linear programs; NP-complete problems; More about NP-completeness; Approximation algorithms; Branch-and-bound and  ...  New and hopefully more transparent reductions are used for many proofs of NP-completeness, and in Chapter 13 a new and simple proof is given that integer linear programming is in NP, based on a discrete  ... 

Page 499 of The Journal of the Operational Research Society Vol. 46, Issue 4 [page]

1995 The Journal of the Operational Research Society  
Although this general problem is NP-complete, it is shown that a restricted version of this problem can be solved in polynomial time.  ...  If A and b are arbitrary, then DMLP can easily be shown to be NP-complete.  ... 

The complexity of linear programming

David P. Dobkin, Steven P. Reiss
1980 Theoretical Computer Science  
Known results are surveyed in order to give -n interesting characterization for the complexity of linear programming and a transformation is given to produce NP-complete versions of LP-complete problems  ...  A notion of LP-completeness is introduced, and a set of problems is shown to be (polynomially) equivalent to linear programming.  ...  the third is likely: i 1) linear programming is NP-complete and NP = co-NP, (2 j linear programming is solvable in polynomial time, (3) linear programming is not in P and is not NP-complete.  ... 
doi:10.1016/0304-3975(80)90031-6 fatcat:py3e62idl5eq3httxbabpzex5q

The Subset Sum Problem: Reducing Time Complexity of NP-Completeness with Quantum Search

Bo Moon
2013 Undergraduate Journal of Mathematical Modeling: One + Two  
The Subset Sum Problem is a member of the NP-complete class, so no known polynomial time algorithm exists for it.  ...  algorithm and Grover's algorithm in solving the Subset Sum Problem, evincing the implications this has on the NP-complete class in general.  ...  that NP-complete problems do have a polynomial time solution.  ... 
doi:10.5038/2326-3652.4.2.2 fatcat:xgpwnxum5jajrmi32fbkylnhay

How hard are n2-hard problems?

Stephen A. Bloch, Jonathan F. Buss, Judy Goldsmith
1994 ACM SIGACT News  
Thus we suggest that these problems are not among the hardest problems solvable in quadratic time.  ...  Many of the \n 2 -hard" problems described by Gajentaan and Overmars can be solved using limited nondeterminism or other sharply-bounded quanti ers.  ...  Introduction One approach to determining the di culty of computational problems is completeness| NP-completeness, exponential-time completeness, etc.  ... 
doi:10.1145/181462.181465 fatcat:in2eefzlvrcxxe32diyiecnahu

Page 2618 of Mathematical Reviews Vol. , Issue 85f [page]

1985 Mathematical Reviews  
When no variable appears in more than three clauses, 3-SAT is trivial and SAT is NP-complete. When no variable appears in more than two clauses, SAT may be solved in linear time.”  ...  NP-completeness is proved by polynomial reduction of the known NP-complete problem “exact cover by 3-sets” to the new problem.  ... 

Intractability results in predicate detection

Sujatha Kashyap, Vijay K. Garg
2005 Information Processing Letters  
It has been shown that global predicate detection in a distributed computation is an NP-complete problem in general.  ...  In particular, we show that there is no polynomial-time algorithm for the detection of linear predicates that do not satisfy the efficient advancement property, unless NP=RP.  ...  The problem of predicate detection has been shown to be NP-complete in general [2] . However, polynomial-time algorithms exist for detecting certain classes of predicates.  ... 
doi:10.1016/j.ipl.2005.02.008 fatcat:scy3kg57qrdwfgjkzedcthwbta

Page 1992 of Mathematical Reviews Vol. , Issue 84e [page]

1984 Mathematical Reviews  
84e:68042 numbers cannot be polynomial time many-one complete in NP (unless P= NP) shows a basic difference between the maximum value problem and many natural NP combinatorial problems.  ...  Other related problems are shown to be NPI (NP-intermediate); i.e., these problems are not known to be in P and are polynomial-time reducible to problems in NP not known to be NP-complete. John T.  ... 

Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron

Komei Fukuda, Thomas M. Liebling, François Margot
1997 Computational geometry  
Some related NP-complete problems associated with a system of linear inequalities are also discussed, including the optimal vertex problems for polyhedra and arrangements of hyperplanes.  ...  algorithm to solve a decision problem, called the restricted vertex problem, for each output, which is shown to be NP-complete.  ...  Acknowledgements The authors are grateful to anonymous referees for their careful reading of the manuscript and many helpful suggestions.  ... 
doi:10.1016/0925-7721(95)00049-6 fatcat:pkascv5iinbihfyp6fxzfxw5de

On the Complexity of Counting the Hilbert Basis of a Linear Diophantine System [chapter]

Miki Hermann, Laurent Juban, Phokion G. Kolaitis
1999 Lecture Notes in Computer Science  
We establish lower and upper bounds on the complexity of this problem by showing that counting the Hilbert basis is #P-hard and belongs to the class #NP.  ...  We investigate the computational complexity of counting the Hilbert basis of a homogeneous system of linear Diophantine equations.  ...  We show that the problem of counting the Hilbert basis is #P-hard and is a member of the class #NP.  ... 
doi:10.1007/3-540-48242-3_2 fatcat:e46mov7eanemhigafonx7kaaji
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