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Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial…
A central approach to algorithmic derandomization is to construct probability distributions with small support that "fool" randomized algorithms, often enabling efficient parallel (NC) implementations. An abstraction of this idea is fooling…
The objective of the present paper is to establish exponential large deviation inequalities, and to use them to show exponential concentration inequalities for the free energy of a polymer in general random environment, its rate of…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
We consider the problem of finding a subgraph of a given graph which maximizes a given function evaluated at its degree sequence. While the problem is intractable already for convex functions, we show that it can be solved in polynomial…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
Finding the most likely (MAP) configuration of a Markov random field (MRF) is NP-hard in general. A promising, recent technique is to reduce the problem to finding a maximum weight stable set (MWSS) on a derived weighted graph, which if…
Matrix concentration inequalities provide a direct way to bound the typical spectral norm of a random matrix. The methods for establishing these results often parallel classical arguments, such as the Laplace transform method. This work…
This paper presents a post-processing algorithm for training fair neural network regression models that satisfy statistical parity, utilizing an explainable singular value decomposition (SVD) of the weight matrix. We propose a linear…
This paper introduces the Nystr\"om PCG algorithm for solving a symmetric positive-definite linear system. The algorithm applies the randomized Nystr\"om method to form a low-rank approximation of the matrix, which leads to an efficient…
We give polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances (up to a fixed upper bound) and efficiently solvable in graphs of bounded treewidth. These schemes apply in all fractionally…
We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We…
One of the main applications of free probability is to show that for appropriately chosen independent copies of $d$ random matrix models, any noncommutative polynomial in these $d$ variables has a spectral distribution that converges…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time algorithm for an arbitrarily good approximation of the optimal value in a large class of Max-2-CSPs parameterised by the class of allowed constraint…
While techniques have been developed for chance constrained stochastic optimal control using sample disturbance data that provide a probabilistic confidence bound for chance constraint satisfaction, far less is known about how to use sample…
We consider the problem of determining the existence of a sequence of matrices driving a discrete-time consensus system to consensus. We transform this problem into one of the existence of a product of the transition (stochastic) matrices…
In this work we consider the problem of maximizing the PageRank of a given target node in a graph by adding $k$ new links. We consider the case that the new links must point to the given target node (backlinks). Previous work shows that…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…