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AverageCase Complexity Theory and PolynomialTime Reductions
, 2001
"... This thesis studies averagecase complexity theory and polynomialtime reducibilities. The issues in averagecase complexity arise primarily from Cai and Selman's extension of Levin's denition of average polynomial time. We study polynomialtime reductions between distributional problems. ..."
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Cited by 2 (0 self)
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This thesis studies averagecase complexity theory and polynomialtime reducibilities. The issues in averagecase complexity arise primarily from Cai and Selman's extension of Levin's denition of average polynomial time. We study polynomialtime reductions between distributional problems
PolynomialTime Reductions, NPCompleteness, and Approximations 1
"... Introduction This course will cover some basic topics in the design and analysis of approximation algorithms. The study of approximation algorithms has developed from the seeming intractability of a number of widelyapplicable NPhard optimization problems. These optimization problems are unlikely ..."
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to admit efficient (polynomialtime computable) optimal solutions. Consequently, a number of techniques have been designed to provide approximate (nearoptimal) solutions that can be obtained efficiently. Of course, we would like to sacrifice as little optimality as possible, while gaining as much
The Relative Power Of Logspace And Polynomial Time Reductions
 Computational Complexity
"... . There exist many different formalisms to model the notion of resource bounded `truthtable' reduction. Most papers in which truthtable reductions appear refer to the seminal paper of Ladner, Lynch and Selman for a definition. The definition of truthtable reductions given there however, p ..."
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Cited by 7 (4 self)
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to the same notion. In particular, we show that coincidence of different notions implies coincidence of complexity classes like NC 1 , LOG, and P , which are widely believed to be different. Key words. reductions; logspace; circuits; branching programs; truthtable; polynomial time. Subject
Polynomialtime reductions from multivariate to bi and univariate integral polynomial factorization
 SIAM J. Comput
, 1985
"... Consider a polynomial f with an arbitrary but fixed number of variables and with integral coefficients. We present an algorithm which reduces the problem of finding the irreducible factors of f in polynomialtime in the total degree of f and the coefficient lengths of f to factoring a univariate int ..."
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Cited by 54 (10 self)
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Consider a polynomial f with an arbitrary but fixed number of variables and with integral coefficients. We present an algorithm which reduces the problem of finding the irreducible factors of f in polynomialtime in the total degree of f and the coefficient lengths of f to factoring a univariate
A PolynomialTime Reduction from Bivariate to Univariate Integral Polynomial Factorization
, 1982
"... n algorithm is presented which reduces the probm lem of finding the irreducible factors of a bivariate polynoial with integer coefficients in polynomial time in the total i degree and the coefficient lengths to factoring a univariate nteger polynomial. Together with A. Lenstra's, H. Lenstra&ap ..."
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Cited by 14 (3 self)
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's u and L. Lovasz' polynomialtime factorization algorithm for nivariate integer polynomials and the author's multivariate  i to bivariate reduction the new algorithm implies the follow ng theorem. Factoring a polynomial with a fixed number of n b variables into irreducibles, except
POLYNOMIALTIME REDUCTIONS FROM MULTIVARIATE TO BI AND UNIVARIATE INTEGRAL POLYNOMIAL FACTORIZATION*
"... Abstract. Consider a polynomial f with an arbitrary but fixed number of variables and with integral coefficients. We present an algorithm which reduces the problem of finding the irreducible factors of f in polynomialtime in the total degree of f and the coefficient lengths of f to factoring a univ ..."
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Abstract. Consider a polynomial f with an arbitrary but fixed number of variables and with integral coefficients. We present an algorithm which reduces the problem of finding the irreducible factors of f in polynomialtime in the total degree of f and the coefficient lengths of f to factoring a
Polynomial Time Reduction from Approximate Shortest Vector Problem to Principal Ideal Problem for Lattices in Some Cyclotomic Rings
, 2015
"... Many cryptographic schemes have been established based on the hardness of lattice problems. For the asymptotic efficiency, ideal lattices in the ring of cyclotomic integers are suggested to be used in most such schemes. On the other hand in computational algebraic number theory one of the main prob ..."
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problem is the principal ideal problem (PIP). Its goal is to find a generator of any principal ideal in the ring of algebraic integers in any number field. In this paper we give a polynomial time reduction from approximate shortest lattice vector problem for principal ideal lattices to their PIP’s
Article A PolynomialTime Reduction from the 3SAT Problem to the Generalized String Puzzle Problem
, 2012
"... algorithms ..."
Polynomial time reduction from 3SAT to solving low first fall degree multivariable cubic equations system
"... degree assumption, the complexity of ECDLP over Fpn where p is small prime and the extension degree n is input size, is subexponential. However, from the recent research, the first fall degree assumption seems to be doubtful. Koster [2] shows that the problem for deciding whether the value of Semaev ..."
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degree assumption is not true. Koster shows the NPcompleteness from the group belonging problem, which is NPcomplete, reduces to the problem for deciding whether the value of Semaev’s formula Sm(x1,..., xm) is 0 or not, in polynomial time. In this paper, from another point of view, we discuss
Results 1  10
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