Related papers: Algorithms for Pattern Containment in 0-1 Matrices
This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices $\text{SO}(n)$. Such problems are nonconvex due to the constraint $X \in \text{SO}(n)$. Nonetheless, we show…
Rearranging the rows or columns of a sparse matrix using an appropriate ordering can significantly reduce fill-ins, i.e., new nonzeros introduced during matrix factorization, decreasing memory usage and runtime. However, finding an ordering…
The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and…
We design a new distribution over $\poly(r \eps^{-1}) \times n$ matrices $S$ so that for any fixed $n \times d$ matrix $A$ of rank $r$, with probability at least 9/10, $\norm{SAx}_2 = (1 \pm \eps)\norm{Ax}_2$ simultaneously for all $x \in…
We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries. This problem is a natural generalization of fundamental problems in combinatorial…
Counting the number of perfect matchings in bipartite graphs, or equivalently computing the permanent of 0-1 matrices, is an important combinatorial problem that has been extensively studied by theoreticians and practitioners alike. The…
We give a proof of the conjecture of Nelson and Nguyen [FOCS 2013] on the optimal dimension and sparsity of oblivious subspace embeddings, up to sub-polylogarithmic factors: For any $n\geq d$ and $\epsilon\geq d^{-O(1)}$, there is a random…
Large-scale subset selection asks for a small useful set of examples, features, sensors, seed users, or context passages from an enormous ground set. Submodular maximization is a canonical model for such diminishing-returns problems, but…
We consider the related tasks of matrix completion and matrix approximation from missing data and propose adaptive sampling procedures for both problems. We show that adaptive sampling allows one to eliminate standard incoherence…
This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…
Computing accurate low rank approximations of large matrices is a fundamental data mining task. In many applications however the matrix contains sensitive information about individuals. In such case we would like to release a low rank…
We study the problem of differentially private continual counting in the unbounded setting where the input size $n$ is not known in advance. Current state-of-the-art algorithms based on optimal instantiations of the matrix mechanism cannot…
In this paper we investigate the parameterized complexity of the task of counting and detecting occurrences of small patterns in unit disk graphs: Given an $n$-vertex unit disk graph $G$ with an embedding of ply $p$ (that is, the graph is…
In this paper we consider graph algorithms in models of computation where the space usage (random accessible storage, in addition to the read only input) is sublinear in the number of edges $m$ and the access to input data is constrained.…
We show that the maximal number of equal entries in a totally positive (resp. totally nonsingular) $n\textrm{-by-}n$ matrix is $\Theta(n^{4/3})$ (resp. $\Theta(n^{3/2}$)). Relationships with point-line incidences in the plane, Bruhat order…
Estimating the linear dimensionality of a data set in the presence of noise is a common problem. However, data may also be corrupted by monotone nonlinear distortion that preserves the ordering of matrix entries but causes linear methods…
Let $A\in\mathbb{R}^{n\times n}$ be a random matrix with independent entries, and suppose that the entries are "uniformly anticoncentrated" in the sense that there is a constant $\varepsilon>0$ such that each entry $a_{ij}$ satisfies…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
In this paper, we give a generalization on the error correcting capability of twisted centralizer codes obtained from a fixed rank 1 matrix. In particular, we fix the combinatorial matrix which is obtained by getting the linear combination…
The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that…