相关论文: Sums of permanental minors using Grassmann algebra

We study the parallel (adaptive) complexity of the classic problem of finding a basis in an $n$-element matroid, given access via an \emph{independence oracle}. In this model, the algorithm may submit polynomially many independence queries…

We present a randomized algorithm for estimating the permanent of an $M \times M$ real matrix $A$ up to an additive error. We do this by viewing the permanent $\mathrm{perm}(A)$ of $A$ as the expectation of a product of centered joint…

In this note, we give explicit expressions of Gauss sums for general (resp. special) linear groups over finite fields, which involves Gauss sums (resp. Kloosterman sums). The key ingredient is averaging such sums over Borel subgroups. As…

We present an algorithm for determining the minimal order differential equations associated to a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths-Dwork pole reduction adapted…

We give an algorithm that for an input n-vertex graph G and integer k>0, in time 2^[O(k)]n either outputs that the treewidth of G is larger than k, or gives a tree decomposition of G of width at most 5k+4. This is the first algorithm…

The zeta and Moebius transforms over the subset lattice of $n$ elements and the so-called subset convolution are examples of unary and binary operations on set functions. While their direct computation requires $O(3^n)$ arithmetic…

A graphical expansion formula for non-commutative matrix integrals with values in a finite-dimensional real or complex von Neumann algebra is obtained in terms of ribbon graphs and their non-orientable counterpart called Moebius graphs. The…

The $k$-cut problem asks, given a connected graph $G$ and a positive integer $k$, to find a minimum-weight set of edges whose removal splits $G$ into $k$ connected components. We give the first polynomial-time algorithm with approximation…

Using an infinite family of generalizations of the Chudnovsky brothers' series recently obtained via the analytic continuation of the Borwein brothers' formula for Ramanujan-type series of level 1, we apply the Gauss-Salamin-Brent iteration…

We present a deterministic algorithm, which, for any given 0< epsilon < 1 and an nxn real or complex matrix A=(a_{ij}) such that | a_{ij}-1| < 0.19 for all i, j computes the permanent of A within relative error epsilon in n^{O(ln n -ln…

We consider ideals involving the maximal minors of a polynomial matrix. For example, those arising in the computation of the critical values of a polynomial restricted to a variety for polynomial optimisation. Gr\"obner bases are a…

We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion. The algorithm recovers an unknown 3-tensor with $r$ incoherent, orthogonal components in…

Many applications, including rank aggregation and crowd-labeling, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and columns. We consider the problem of estimating such a matrix based on…

There are two widely used models for the Grassmannian $\operatorname{Gr}(k,n)$, as the set of equivalence classes of orthogonal matrices $\operatorname{O}(n)/(\operatorname{O}(k) \times \operatorname{O}(n-k))$, and as the set of trace-$k$…

The modular subset sum problem consists of deciding, given a modulus $m$, a multiset $S$ of $n$ integers in $0..m-1$, and a target integer $t$, whether there exists a subset of $S$ with elements summing to $t \mod m $, and to report such a…

A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…

The conjugation action of the complex orthogonal group on the polynomial functions on $n \times n$ matrices gives rise to a graded algebra of invariant polynomials. A spanning set of this algebra is in bijective correspondence to a set of…

We introduce a natural definition for sums of the form \[ \sum_{\nu=1}^x f(\nu) \] when the number of terms x is a rather arbitrary real or even complex number. The resulting theory includes the known interpolation of the factorial by the…

Updating a linear least squares solution can be critical for near real-time signalprocessing applications. The Greville algorithm proposes a simple formula for updating the pseudoinverse of a matrix A $\in$ R nxm with rank r. In this paper,…

Min-plus product of two $n\times n$ matrices is a fundamental problem in algorithm research. It is known to be equivalent to APSP, and in general it has no truly subcubic algorithms. In this paper, we focus on the min-plus product on a…