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A Variable-Complexity Norm Maximization Problem

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*. ...

##
###
Some Dichotomy Theorems for Neural Learning Problems

2004
*
Journal of machine learning research
*

We determine for each

dblp:journals/jmlr/Schmitt04
fatcat:bl3cwzg7xbbr7lzgl4qk37edam
*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. ...##
###
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

1995
*
Journal of the Operational Research Society
*

Although this general

doi:10.2307/2584597
fatcat:yzgghw34tbac3ok3baazbupeei
*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*. ...##
###
On the inherent intractability of certain coding problems (Corresp.)

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

doi:10.1109/tit.1978.1055873
fatcat:sepkw4wkcndknjvrec2l3z7yyy
*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*...##
###
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

1980
*
Theoretical Computer Science
*

Known results are surveyed in order to give -n interesting characterization for the complexity of

doi:10.1016/0304-3975(80)90031-6
fatcat:py3e62idl5eq3httxbabpzex5q
*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*. ...##
###
The Subset Sum Problem: Reducing Time Complexity of NP-Completeness with Quantum Search

2013
*
Undergraduate Journal of Mathematical Modeling: One + Two
*

The Subset Sum

doi:10.5038/2326-3652.4.2.2
fatcat:xgpwnxum5jajrmi32fbkylnhay
*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. ...##
###
How hard are n2-hard problems?

1994
*
ACM SIGACT News
*

Thus we suggest that these

doi:10.1145/181462.181465
fatcat:in2eefzlvrcxxe32diyiecnahu
*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. ...##
###
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

2005
*
Information Processing Letters
*

It has been shown that global predicate detection in a distributed computation is an

doi:10.1016/j.ipl.2005.02.008
fatcat:scy3kg57qrdwfgjkzedcthwbta
*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. ...##
###
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

1997
*
Computational geometry
*

Some related

doi:10.1016/0925-7721(95)00049-6
fatcat:pkascv5iinbihfyp6fxzfxw5de
*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. ...##
###
On the Complexity of Counting the Hilbert Basis of a Linear Diophantine System
[chapter]

1999
*
Lecture Notes in Computer Science
*

We establish lower

doi:10.1007/3-540-48242-3_2
fatcat:e46mov7eanemhigafonx7kaaji
*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*. ...
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