All reports by Author Gábor Ivanyos:

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TR17-016
| 31st January 2017
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Vishwas Bhargava, Gábor Ivanyos, Rajat Mittal, Nitin Saxena#### Irreducibility and deterministic r-th root finding over finite fields

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TR14-034
| 3rd March 2014
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Gábor Ivanyos, Raghav Kulkarni, Youming Qiao, Miklos Santha, Aarthi Sundaram#### On the complexity of trial and error for constraint satisfaction problems

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TR13-103
| 24th July 2013
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Gábor Ivanyos, Marek Karpinski, Youming Qiao, Miklos Santha#### Generalized Wong sequences and their applications to Edmonds' problems

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TR12-068
| 25th May 2012
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Manuel Arora, Gábor Ivanyos, Marek Karpinski, Nitin Saxena#### Deterministic Polynomial Factoring and Association Schemes

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TR09-058
| 4th July 2009
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Gábor Ivanyos, Marek Karpinski, Nitin Saxena#### Deterministic Polynomial Time Algorithms for Matrix Completion Problems

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TR08-099
| 19th November 2008
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Gábor Ivanyos, Marek Karpinski, Lajos Rónyai, Nitin Saxena#### Trading GRH for algebra: algorithms for factoring polynomials and related structures

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TR08-043
| 12th April 2008
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Gábor Ivanyos, Marek Karpinski, Nitin Saxena#### Schemes for Deterministic Polynomial Factoring

Vishwas Bhargava, Gábor Ivanyos, Rajat Mittal, Nitin Saxena

Constructing $r$-th nonresidue over a finite field is a fundamental computational problem. A related problem is to construct an irreducible polynomial of degree $r^e$ (where $r$ is a prime) over a given finite field $\F_q$ of characteristic $p$ (equivalently, constructing the bigger field $\F_{q^{r^e}}$). Both these problems have famous randomized ... more >>>

Gábor Ivanyos, Raghav Kulkarni, Youming Qiao, Miklos Santha, Aarthi Sundaram

In a recent work of Bei, Chen and Zhang (STOC 2013), a trial and error model of computing was introduced, and applied to some constraint satisfaction problems. In this model the input is hidden by an oracle which, for a candidate assignment, reveals some information about a violated constraint if ... more >>>

Gábor Ivanyos, Marek Karpinski, Youming Qiao, Miklos Santha

We design two deterministic polynomial time algorithms for variants of a problem introduced by Edmonds in 1967: determine the rank of a matrix $M$ whose entries are homogeneous linear polynomials over the integers. Given a linear subspace $\mathcal{B}$ of the $n \times n$ matrices over some field $\mathbb{F}$, we consider ... more >>>

Manuel Arora, Gábor Ivanyos, Marek Karpinski, Nitin Saxena

The problem of finding a nontrivial factor of a polynomial $f(x)$ over a finite field $\mathbb{F}_q$ has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the generalized Riemann hypothesis (GRH). In this work we improve the state of the ... more >>>

Gábor Ivanyos, Marek Karpinski, Nitin Saxena

We present new deterministic algorithms for several cases of the maximum rank matrix completion

problem (for short matrix completion), i.e. the problem of assigning values to the variables in

a given symbolic matrix as to maximize the resulting matrix rank. Matrix completion belongs to

the fundamental problems in computational complexity ...
more >>>

Gábor Ivanyos, Marek Karpinski, Lajos Rónyai, Nitin Saxena

In this paper we develop techniques that eliminate the need of the Generalized

Riemann Hypothesis (GRH) from various (almost all) known results about deterministic

polynomial factoring over finite fields. Our main result shows that given a

polynomial f(x) of degree n over a finite field k, we ...
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Gábor Ivanyos, Marek Karpinski, Nitin Saxena

In this work we relate the deterministic

complexity of factoring polynomials (over

finite

fields) to certain combinatorial objects we

call

m-schemes. We extend the known conditional

deterministic subexponential time polynomial

factoring algorithm for finite fields to get an

underlying m-scheme. We demonstrate ...
more >>>