Related papers: A Generalization of the Random Assignment Problem

We introduce and study the problem of consistent low-rank approximation, in which rows of an input matrix $\mathbf{A}\in\mathbb{R}^{n\times d}$ arrive sequentially and the goal is to provide a sequence of subspaces that well-approximate the…

The ranking and selection problem is a popular framework in the simulation literature for studying optimal information collection. We study a version of this problem in which the simulation output for each design is normally distributed…

We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…

We analyse a generalisation of the Quicksort algorithm, where k uniformly at random chosen pivots are used for partitioning an array of n distinct keys. Specifically, the expected cost of this scheme is obtained, under the assumption of…

For a family X of k-subsets of the set 1,...,n, let |X| be the cardinality of X and let Gamma(X,mu) be the expected maximum weight of a subset from X when the weights of 1,...,n are chosen independently at random from a symmetric…

We consider models of assignment for random $N$ blue points and $N$ red points on an interval of length $2N$, in which the cost for connecting a blue point in $x$ to a red point in $y$ is the concave function $|x-y|^p$, for $0<p<1$.…

The $k$-of-$n$ testing problem involves performing $n$ independent tests sequentially, in order to determine whether/not at least $k$ tests pass. The objective is to minimize the expected cost of testing. This is a fundamental and…

This work studies discrete-time discounted Markov decision processes with continuous state and action spaces and addresses the inverse problem of inferring a cost function from observed optimal behavior. We first consider the case in which…

In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…

Given vectors $v_1,\dots,v_n\in\mathbb{R}^d$ and a matroid $M=([n],I)$, we study the problem of finding a basis $S$ of $M$ such that $\det(\sum_{i \in S}v_i v_i^\top)$ is maximized. This problem appears in a diverse set of areas such as…

The random assignment problem asks for the minimum-cost perfect matching in the complete $n\times n$ bipartite graph $\Knn$ with i.i.d. edge weights, say uniform on $[0,1]$. In a remarkable work by Aldous (2001), the optimal cost was shown…

Given $n$ integer, let $X$ be either the set of hermitian or real $n\times n$ matrices of rank at least $n-1$. If $n$ is even, we give a sharp estimate on the maximal dimension of a real vector subspace of $X\cup\{0\}$. The rusults are…

In $masked\ low-rank\ approximation$, one is given $A \in \mathbb{R}^{n \times n}$ and binary mask matrix $W \in \{0,1\}^{n \times n}$. The goal is to find a rank-$k$ matrix $L$ for which: $$cost(L) = \sum_{i=1}^{n} \sum_{j = 1}^{n} W_{i,j}…

We study the problem of computing maximin share guarantees, a recently introduced fairness notion. Given a set of $n$ agents and a set of goods, the maximin share of a single agent is the best that she can guarantee to herself, if she would…

For many constraint satisfaction problems, the algorithm which chooses a random assignment achieves the best possible approximation ratio. For instance, a simple random assignment for {\sc Max-E3-Sat} allows 7/8-approximation and for every…

This work examines the expected computational cost to determine an approximate global minimum of a class of cost functions characterized by the variance of coefficients. The cost function takes $N$-dimensional binary states as arguments and…

Let $\mathbf{A}_{n,m;k}$ be a random $n \times m$ matrix with entries from some field $\mathbb{F}$ where there are exactly $k$ non-zero entries in each column, whose locations are chosen independently and uniformly at random from the set of…

In many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data. More specifically, if we have a set of $N$ independent, identically distributed measurements of an $M$…

We consider the set Sigma(R,C) of all mxn matrices having 0-1 entries and prescribed row sums R=(r_1, ..., r_m) and column sums C=(c_1, ..., c_n). We prove an asymptotic estimate for the cardinality |Sigma(R, C)| via the solution to a…

We consider the synthesis problem of Compressed Sensing - given s and an MXn matrix A, extract from it an mXn submatrix A', certified to be s-good, with m as small as possible. Starting from the verifiable sufficient conditions of…