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Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal…
We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…
The 3-domatic number problem asks whether a given graph can be partitioned intothree dominating sets. We prove that this problem can be solved by a deterministic algorithm in time 2.695^n (up to polynomial factors). This result improves the…
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…
A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few…
The current paper investigates the bounded distance decoding (BDD) problem for ensembles of lattices whose generator matrices have sub-Gaussian entries. We first prove that, for these ensembles the BDD problem is NP-hard in the worst case.…
The $k$-CombDMR problem is that of determining whether an $n \times n$ distance matrix can be realised by $n$ vertices in some undirected graph with $n + k$ vertices. This problem has a simple solution in the case $k=0$. In this paper we…
In this paper, we propose and analyze iterative method based on projection techniques to solve a non-singular linear system Ax = b. In particular, for a given positive integer m, m-dimensional successive projection method (mD-SPM) for…
Let $C$ be an arithmetic circuit of $poly(n)$ size given as input that computes a polynomial $f\in\mathbb{F}[X]$, where $X=\{x_1,x_2,\ldots,x_n\}$ and $\mathbb{F}$ is any field where the field arithmetic can be performed efficiently. We…
Boolean-width is a recently introduced graph parameter. Many problems are fixed parameter tractable when parametrized by boolean-width, for instance "Minimum Weighted Dominating Set" (MWDS) problem can be solved in $O^*(2^{3k})$ time given…
A randomized algorithm for a search problem is *pseudodeterministic* if it produces a fixed canonical solution to the search problem with high probability. In their seminal work on the topic, Gat and Goldwasser posed as their main open…
We study a type of Riemannian gradient descent (RGD) algorithm, designed through Riemannian preconditioning, for optimization on $\mathcal{M}_k^{m\times n}$ -- the set of $m\times n$ real matrices with a fixed rank $k$. Our analysis is…
In this paper we present a new algorithm for solving linear programs that requires only $\tilde{O}(\sqrt{rank(A)}L)$ iterations to solve a linear program with $m$ constraints, $n$ variables, and constraint matrix $A$, and bit complexity…
In the total matching problem, one is given a graph $G$ with weights on the vertices and edges. The goal is to find a maximum weight set of vertices and edges that is the non-incident union of a stable set and a matching. We consider the…
We consider the additive version of the matrix denoising problem, where a random symmetric matrix $S$ of size $n$ has to be inferred from the observation of $Y=S+Z$, with $Z$ an independent random matrix modeling a noise. For prior…
We present a new algorithm that, given two matrices in $GL(n,Q)$, decides if they are conjugate in $GL(n,Z)$ and, if so, determines a conjugating matrix. We also give an algorithm to construct a generating set for the centraliser in…
In this paper, we present a generic parametrization of generically zero-dimensional parametric polynomial systems. More specifically, we study the specialization properties of the Rational Univariate Representation and derive bounds on the…
Barvinok introduced the symmetrized determinant ($\sdet$) as a \emph{non-commutative} analogue of the determinant. Intuitively, given a square matrix over an associative algebra, we can obtain the symmetrized determinant by averaging over…
We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in $\Sigma_2^p$. In the case of linear matroids, which are represented over polynomially growing fields, we note that the problem is…
The minimum rank of a graph G is the minimum rank over all real symmetric matrices whose off-diagonal sparsity pattern is the same as that of the adjacency matrix of G. In this note we present the first exact algorithm for the minimum rank…