Related papers: A polynomial time algorithm for local testability …
This article deals with new polynomial time algorithm for graph isomorphism testing.
Group testing is a well-known search problem that consists in detecting of $s$ defective members of a set of $t$ samples by carrying out tests on properly chosen subsets of samples. In classical group testing the goal is to find all…
In this paper, we introduce a variation of the group testing problem capturing the idea that a positive test requires a combination of multiple ``types'' of item. Specifically, we assume that there are multiple disjoint \emph{semi-defective…
Testing efficiently whether a finite set with a binary operation over it, given as an oracle, is a group is a well-known open problem in the field of property testing. Recently, Friedl, Ivanyos and Santha have made a significant step in the…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
In this paper we consider the problem of testing whether two finite groups are isomorphic. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of…
In [Phys. Rev. A 69, 022316 (2004)] we presented a description of the action of local Clifford operations on graph states in terms of a graph transformation rule, known in graph theory as \emph{local complementation}. It was shown that two…
In this paper, we devise two algorithms for the problem of testing $q$-monomials of degree $k$ in any multivariate polynomial represented by a circuit, regardless of the primality of $q$. One is an $O^*(2^k)$ time randomized algorithm. The…
L.A. Shemetkov posed a Problem 9.74 in Kourovka Notebook to find all local formations $\mathfrak{F}$ of finite groups such that every finite minimal non-$\mathfrak{F}$-group is either a Schmidt group or a group of prime order. All known…
This paper introduces a problem in which the state of a system needs to be determined through costly tests of its components by a limited number of testing units and before a given deadline. We also consider a closely related search problem…
We give a deterministic polynomial-time algorithm to check whether the Galois group $\Gal{f}$ of an input polynomial $f(X) \in \Q[X]$ is nilpotent: the running time is polynomial in $\size{f}$. Also, we generalize the Landau-Miller…
A semi-algebraic set is a subset of $\mathbb{R}^n$ defined by a finite collection of polynomial equations and inequalities. In this paper, we investigate the problem of determining whether two points in such a set belong to the same…
A CM-order is a reduced order equipped with an involution that mimics complex conjugation. The Witt-Picard group of such an order is a certain group of ideal classes that is closely related to the "minus part" of the class group. We present…
We give a strongly polynomial time algorithm which determines whether or not a bivariate polynomial is real stable. As a corollary, this implies an algorithm for testing whether a given linear transformation on univariate polynomials…
The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite strings over some finite alphabet) are in the same…
Finding the minimum of a multivariate real polynomial is a well-known hard problem with various applications. We present a polynomial time algorithm to approximate such lower bounds via sums of nonnegative circuit polynomials (SONC). As a…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
A decision problem is called parameterized if its input is a pair of strings. One of these strings is referred to as a parameter. The problem: given a propositional logic program P and a non-negative integer k, decide whether P has a stable…
As a partial answer to a question of Rao, a deterministic and customizable efficient algorithm is presented to test whether an arbitrary graphical degree sequence has a bipartite realization. The algorithm can be configured to run in…
The mixedness of one share of a pure bipartite state determines whether the overall state is a separable, unentangled state. Here we consider quantum computational tests of mixedness, and we derive an exact expression of the acceptance…