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The complexity of approximating a nonlinear program

Mihir Bellare, Phillip Rogaway
1995 Mathematical programming  
We show that there is no polynomial time approximation algorithm for this problem, even one with a very poor guarantee, unless P = NP.  ...  As with NP-hard problems in combinatorial optimization, interest is turning to the development of (efficient) approximation algorithms-algorithms which run in polynomial time and find a solution not too  ...  We thank an anonymous referee for comments.  ... 
doi:10.1007/bf01585569 fatcat:jmegfrb7v5flpiquskl6r7o67a

The Complexity of Approximating a Nonlinear Program [chapter]

Mihir Bellare, Phillip Rogaway
1993 Complexity in Numerical Optimization  
We show that there is no polynomial time approximation algorithm for this problem, even one with a very poor guarantee, unless P = NP.  ...  As with NP-hard problems in combinatorial optimization, interest is turning to the development of (efficient) approximation algorithms-algorithms which run in polynomial time and find a solution not too  ...  We thank an anonymous referee for comments.  ... 
doi:10.1142/9789814354363_0002 fatcat:foxxtsqz35bfdcchech42f7bcm

Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs [article]

Ryan L. Mann, Michael J. Bremner
2018 arXiv   pre-print
Our algorithm is based on an approach due to Barvinok for approximating evaluations of a polynomial based on the location of the complex zeros and a technique due to Patel and Regts for efficiently computing  ...  We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions and external fields are absolutely bounded close to zero.  ...  Now observe that an additive approximation of the logarithm of a polynomial corresponds to a multiplicative approximation of the polynomial.  ... 
arXiv:1806.11282v1 fatcat:cyuqsil4bbe2ffzcscupsis26a

Computational communicative algebra

Hennie Poulisse
2006 Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06  
This is accomplished through an Approximate Border Basis Algorithm.  ...  An interpretation of the Approximate Vanishing Ideal is that it reveals polynomial identities that are almost satisfied over the set of points under consideration.  ... 
doi:10.1145/1145768.1145771 dblp:conf/issac/Poulisse06 fatcat:hbkgd5rpwnghzb6ejxnxkbi3aa

Fast Evaluation of Radial Basis Functions: Moment-Based Methods

R. K. Beatson, G. N. Newsam
1998 SIAM Journal on Scientific Computing  
Adaptive polynomial approximation. In this section we outline an adaptive method for constructing the polynomial approximations to φ required at various stages in the algorithm.  ...  Calculate an error polynomial approximation q 2 to φ on the interval [ 1 4 , 1]. Set = 2 and h 2 = degree(q 2 ). Step 2 If there are panels at level Create interaction and peer lists.  ...  Table 2 Degree of the economized polynomial sufficient to yield the specified absolute accuracy when approximating φ on the given interval. φ Interval Accuracy From equations (B.1), (B.2), and the uniqueness  ... 
doi:10.1137/s1064827595293569 fatcat:5nz2h2cusvht3bwcns4sy3zv3m

Factoring games to isolate strategic interactions

George B. Davis, Michael Benisch, Kathleen M. Carley, Norman M. Sadeh
2007 Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems - AAMAS '07  
We give an expected polynomial time algorithm to divide a boundedpayout normal form game into factor games that isolate independent strategic interactions.  ...  We also show that the best approximate factoring can be found in polynomial time for a specific interaction that is not fully independent.  ...  We outlined a polynomial time algorithm for finding the minimal ǫ-factoring that isolates a specific interaction.  ... 
doi:10.1145/1329125.1329207 dblp:conf/atal/DavisBCS07 fatcat:net5zroknzg35h7iaglhrgstve

Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs

Ryan L. Mann, Michael J. Bremner
2019 Quantum  
Our algorithm is based on an approach due to Barvinok for approximating evaluations of a polynomial based on the location of the complex zeros and a technique due to Patel and Regts for efficiently computing  ...  We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions and external fields are absolutely bounded close to zero.  ...  Now observe that an additive approximation of the logarithm of a polynomial corresponds to a multiplicative approximation of the polynomial.  ... 
doi:10.22331/q-2019-07-11-162 fatcat:po75rwjtkfcrzgr2iock3f3fwi

On the approximation of protein threading

Tatsuya Akutsu, Satoru Miyano
1997 Proceedings of the first annual international conference on Computational molecular biology - RECOMB '97  
Since this problem was already proved to be NP-hard, we study polynomial time approximation algorithms.  ...  We also show approximation algorithms for a special case and a general case, where a graph representing interactions between amino acid residues is restricted to be planar in a special case.  ...  Identifying B-strands is also an important problem in molecular biology. In this paper, we consider polynomial time approximation algorithms.  ... 
doi:10.1145/267521.267523 dblp:conf/recomb/AkutsuM97 fatcat:6ivdlmrhffdopf5hgpoiwhn2dm

On the approximation of protein threading

Tatsuya Akutsu, Satoru Miyano
1999 Theoretical Computer Science  
Since this problem was already proved to be NP-hard, we study polynomial time approximation algorithms.  ...  We also show approximation algorithms for a special case and a general case, where a graph representing interactions between amino acid residues is restricted to be planar in a special case.  ...  Identifying B-strands is also an important problem in molecular biology. In this paper, we consider polynomial time approximation algorithms.  ... 
doi:10.1016/s0304-3975(98)00089-9 fatcat:pnalsqloonfddejq42mslhocqm

Generating function approximations at compile time

Jean-Michel Muller
2006 2006 Fortieth Asilomar Conference on Signals, Systems and Computers  
This may have some drawbacks: first in frequent cases, it is a compound function (e.g. log(1 + exp(−x))) that is needed, so that directly building a polynomial or rational approximation for that function  ...  We investigate the possibility of directly building accurate approximations at compile-time.  ...  ACKNOWLEDGEMENTS Nicolas Brisebarre, Sylvain Chevillard and Christoph Lauter provided some of the examples presented here, and did a great work on polynomial approximation generation.  ... 
doi:10.1109/acssc.2006.354761 fatcat:sbuqgbyxlzg3pbq7vo3rmaemh4

Computational complexity of loss networks

Graham Louth, Michael Mitzenmacher, Frank Kelly
1994 Theoretical Computer Science  
We also show that a general algorithm for approximating the blocking probabilities is also intractable unless RP=NP, which seems unlikely according to current common notions in complexity theory.  ...  In this paper we examine the theoretical limits on developing algorithms to find blocking probabilities in a general loss network.  ...  Suppose such an algorithm existed. Then we use it to create an fpras for l/( 1 -L,) as follows. Given an E', approximate L, with the algorithm above using E = &l/2.  ... 
doi:10.1016/0304-3975(94)90293-3 fatcat:44z3vrhzvjaebmp4jidukaq4lu

Approximability of the Ground State Problem for Certain Ising Spin Glasses

Alberto Bertoni, Paola Campadelli, Cristina Gangai, Roberto Posenato
1997 Journal of Complexity  
There is an approximate polynomial time algorithm with absolute error less than n γ for all n; there exists a constant β > 0 such that every approximate polynomial time algorithm has absolute error greater  ...  There is an approximate polynomial time algorithm with absolute error less than n/lg n; there exists a number k > 1 such that every approximate polynomial time algorithm has absolute error greater than  ...  Given a polynomial-time approximation algorithm A for GROUND STATE(γ), we construct an algorithm A for GROUND STATE( 1 2 ) as follows. ALGORITHM A .  ... 
doi:10.1006/jcom.1997.0449 fatcat:ghrd2c2ufzbufpkicsfwzaymle

Sparse pseudorandom distributions

Oded Goldreich, Hugo Krawczyk
1992 Random structures & algorithms (Print)  
polynomial-time algorithms.  ...  Any polynomial-time algorithm trying to find a string in their support will succeed with negligible probability.  ...  We say that an interactive proof is zero-knowledge if for all probabilistic polynomial-time machines V * , there exists a probabilistic polynomial-time algorithm Mr (called a sirnulafor) that on input  ... 
doi:10.1002/rsa.3240030206 fatcat:cfywwwbbr5as5mcm7fm2lvai7y

Complexity of Discrete Energy Minimization Problems [article]

Mengtian Li, Alexander Shekhovtsov, Daniel Huber
2016 arXiv   pre-print
This paper can help vision researchers to select an appropriate model for an application or guide them in designing new algorithms.  ...  This finding rules out the existence of any approximation algorithm with a sub-exponential approximation ratio in the input size for these two problems, including constant factor approximations.  ...  Given an optimization problem P = (I, S, m, goal) an algorithm A is an approximation algorithm for P if, for any given instance x ∈ I, it returns an approximate solution, that is a feasible solution A(  ... 
arXiv:1607.08905v1 fatcat:k5xddu3xvndnziljktxo5p4mpe

Modeling opponent decision in repeated one-shot negotiations

Sabyasachi Saha, Anish Biswas, Sandip Sen
2005 Proceedings of the fourth international joint conference on Autonomous agents and multiagent systems - AAMAS '05  
In this paper, we present a learning mechanism using Chebychev's polynomials by which an agent can approximately model the decision function used by the other agent based on the decision history of its  ...  Typically, these interactions take place under incomplete information, i.e., an agent does not know exactly which offers may be acceptable to its opponent or what other outside options are available to  ...  Acknowledgements: This work has been supported in part by an NSF award IIS-0209208.  ... 
doi:10.1145/1082473.1082534 dblp:conf/atal/SahaBS05 fatcat:x2e3gfb4bvcu3jwhp7mt3gxbua
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