Related papers: On Factorization of Sparse Polynomials of Bounded …
Cartesian products of graphs and hypergraphs have been studied since the 1960s. For (un)directed hypergraphs, unique \emph{prime factor decomposition (PFD)} results with respect to the Cartesian product are known. However, there is still a…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
For the General Factor problem we are given an undirected graph $G$ and for each vertex $v\in V(G)$ a finite set $B_v$ of non-negative integers. The task is to decide if there is a subset $S\subseteq E(G)$ such that $deg_S(v)\in B_v$ for…
Let $f, f_1, \ldots, f_\nV$ be polynomials with rational coefficients in the indeterminates $\bfX=X_1, \ldots, X_n$ of maximum degree $D$ and $V$ be the set of common complex solutions of $\F=(f_1,\ldots, f_\nV)$. We give an algorithm…
Computational problem certificates are additional data structures for each output, which can be used by a-possibly randomized-verification algorithm that proves the correctness of each output. In this paper, we give an algorithm that…
We propose an algorithm for deterministic continuous Markov Decision Processes with sparse rewards that computes the optimal policy exactly with no dependency on the size of the state space. The algorithm has time complexity of $O( |R|^3…
In this paper we study polynomial identity testing of sums of $k$ read-once algebraic branching programs ($\Sigma_k$-RO-ABPs), generalizing the work in (Shpilka and Volkovich 2008,2009), who considered sums of $k$ read-once formulas…
In this paper we study the Product Partition Problem (PPP), i.e. we are given a set of $n$ natural numbers represented on $m$ bits each and we are asked if a subset exists such that the product of the numbers in the subset equals the…
We give deterministic black-box polynomial identity testing algorithms for multilinear read-once oblivious algebraic branching programs (ROABPs), in n^(lg^2 n) time. Further, our algorithm is oblivious to the order of the variables. This is…
Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…
A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective $\sum_{ij\in E} C_{ij}(f_{ij})$ over feasible flows $f$, where on every arc $ij$ of the network, $C_{ij}$ is a convex function. We give a…
Here, we give an algorithm for deciding if the nonnegative rank of a matrix $M$ of dimension $m \times n$ is at most $r$ which runs in time $(nm)^{O(r^2)}$. This is the first exact algorithm that runs in time singly-exponential in $r$. This…
In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…
In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower…
We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds to a vertex of the graph and edges in the graph represent…
We develop a fast algorithm for computing the bound of an Ore polynomial over a skew field, under mild conditions. As an application, we state a criterion for deciding whether a bounded Ore polynomial is irreducible, and we discuss a…
In our recent work \cite{StojnicCSetam09} we considered solving under-determined systems of linear equations with sparse solutions. In a large dimensional and statistical context we proved that if the number of equations in the system is…
Sparse PCA is one of the most well-studied problems in high-dimensional statistics. In this problem, we are given samples from a distribution with covariance $\Sigma$, whose top eigenvector $v \in R^d$ is $s$-sparse. Existing sparse PCA…
We give reconstruction algorithms for subclasses of depth-3 arithmetic circuits. In particular, we obtain the first efficient algorithm for finding tensor rank, and an optimal tensor decomposition as a sum of rank-one tensors, when given…
We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…