Related papers: A Polynomial-time Algorithm for Computing the Perm…
We identify and study relevant structural parameters for the problem PerfMatch of counting perfect matchings in a given input graph $G$. These generalize the well-known tractable planar case, and they include the genus of $G$, its apex…
In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…
We are concerned with the problem of decomposing the parameter space of a parametric system of polynomial equations, and possibly some polynomial inequality constraints, with respect to the number of real solutions that the system attains.…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time--space complexity is roughly quadratic in the logarithm of the…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
A fast algorithm is presented for determining the linear complexity and the minimal polynomial of periodic sequences over GF(q) with period q n p m, where p is a prime, q is a prime and a primitive root modulo p2. The algorithm presented…
The problem of finding a nontrivial factor of a polynomial f(x) over a finite field F_q has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the…
For fixed compact connected Lie groups H \subseteq G, we provide a polynomial time algorithm to compute the multiplicity of a given irreducible representation of H in the restriction of an irreducible representation of G. Our algorithm is…
This paper presents a new anytime algorithm for the marginal MAP problem in graphical models. The algorithm is described in detail, its complexity and convergence rate are studied, and relations to previous theoretical results for the…
We present a method of representing an element of $\mathbb{F}_3^n$ as an element of $\mathbb{F}_n^2 \times \mathbb{F}_n^2$ which in practice will be a pair of unsigned integers. We show how to do addition, subtraction and pointwise…
We prove a characterization of all polynomial-time computable queries on the class of interval graphs by sentences of fixed-point logic with counting. More precisely, it is shown that on the class of unordered interval graphs, any query is…
We design a deterministic polynomial time $c^n$ approximation algorithm for the permanent of positive semidefinite matrices where $c=e^{\gamma+1}\simeq 4.84$. We write a natural convex relaxation and show that its optimum solution gives a…
In this paper, we present a new method for computing bounded-degree factors of lacunary multivariate polynomials. In particular for polynomials over number fields, we give a new algorithm that takes as input a multivariate polynomial f in…
The synthesis of classical Computational Complexity Theory with Recursive Analysis provides a quantitative foundation to reliable numerics. Here the operators of maximization, integration, and solving ordinary differential equations are…
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…
We present novel algorithms to factor polynomials over a finite field $\F_q$ of odd characteristic using rank $2$ Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomial…
Let $\mathbb{F}_q$ be a finite field with $q$ elements. M. Gerstenhaber and Irving Reiner has given two different methods to show the number of matrices with a given characteristic polynomial. In this talk, we will give another proof for…
In this work, we study the computational complexity of quantum determinants, a $q$-deformation of matrix permanents: Given a complex number $q$ on the unit circle in the complex plane and an $n\times n$ matrix $X$, the $q$-permanent of $X$…
Littlewood-Richardson, Kronecker and plethysm coefficients are fundamental multiplicities of interest in Representation Theory and Algebraic Combinatorics. Determining a combinatorial interpretation for the Kronecker and plethysm…