Related papers: On a Problem Posed by Maurice Nivat
The scattering equations, recently proposed by Cachazo, He and Yuan as providing a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension (including scalars, gauge bosons and gravitons), are…
Motivated by problems of comparative genomics and paleogenomics, in [Chauve et al., 2009], the authors introduced the Gapped Consecutive-Ones Property Problem (k,delta)-C1P: given a binary matrix M and two integers k and delta, can the…
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 call a matrix completely mixable if the entries in its columns can be permuted so that all row sums are equal. If it is not completely mixable, we want to determine the smallest maximal and largest minimal row sum attainable. These…
We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: (*) Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In…
Modular composition is the problem of computing the composition of two univariate polynomials modulo a third one. For a long time, the fastest algebraic algorithm for this problem was that of Brent and Kung (1978). Recently, we improved…
This paper addresses the numerical solution of the matrix square root problem. Two fixed point iterations are proposed by rearranging the nonlinear matrix equation $A - X^2 = 0$ and incorporating a positive scaling parameter. The proposals…
Let $ K $ be a number field, $ S $ a finite set of places of $ K $, and $ \mathcal{O}_S $ be the ring of $ S $-integers. Moreover, let $$ G_n^{(0)} Z^d + \cdots + G_n^{(d-1)} Z + G_n^{(d)} $$ be a polynomial in $ Z $ having simple linear…
We consider the NP-hard 2-period balanced travelling salesman problem. In this problem the salesman needs to visit a set of customers in two time periods. A given subset of the customers has to be visited in both periods while the rest of…
We propose an algorithm for deciding whether a given braid is pseudo-Anosov, reducible, or periodic. The algorithm is based on Garside's weighted decomposition and is polynomial-time in the word-length of an input braid. Moreover, a…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
In this paper we study the {\it bilinear assignment problem} (BAP) with size parameters $m$ and $n$, $m\leq n$. BAP is a generalization of the well known quadratic assignment problem and the three dimensional assignment problem and hence…
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…
We consider the problem of summarizing a multi set of elements in $\{1, 2, \ldots , n\}$ under the constraint that no element appears more than $\ell$ times. The goal is then to answer \emph{rank} queries --- given $i\in\{1, 2, \ldots ,…
We show that finding minimally intersecting $n$ paths from $s$ to $t$ in a directed graph or $n$ perfect matchings in a bipartite graph can be done in polynomial time. This holds more generally for unimodular set systems.
Given an integer $n\geq 1$ and an irreducible character $\chi_{\lambda}$ of $S_{n}$ for some partition $\lambda$ of $n$, the immanant $\mathrm{imm}_{\lambda}:\mathbb{C}^{n\times n}\to\mathbb{C}$ maps matrices $A\in\mathbb{C}^{n\times n}$ to…
Let $M$ be a real $r\times c$ matrix and let $k$ be a positive integer. In the column subset selection problem (CSSP), we need to minimize the quantity $\|M-SA\|$, where $A$ can be an arbitrary $k\times c$ matrix, and $S$ runs over all…
The problem of extending partial geometric graph representations such as plane graphs has received considerable attention in recent years. In particular, given a graph $G$, a connected subgraph $H$ of $G$ and a drawing $\mathcal{H}$ of $H$,…
NP complete problem is one of the most challenging issues. The question of whether all problems in NP are also in P is generally considered one of the most important open questions in mathematics and theoretical computer science as it has…
The feedback class of a locally Brunovsky linear system is fully determined by the decomposition of state space as direct sum of system invariants [4]. In this paper we attack the problem of enumerating all feedback classes of locally…