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Ge and Stefankovic have recently introduced a novel two-variable graph polynomial. When specialised to a bipartite graphs G and evaluated at the point (1/2,1) this polynomial gives the number of independent sets in the graph. Inspired by…
We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
The potential for machine learning systems to amplify social inequities and unfairness is receiving increasing popular and academic attention. Much recent work has focused on developing algorithmic tools to assess and mitigate such…
Analysis of algorithms on time-varying networks (often called evolving graphs) is a modern challenge in theoretical computer science. The edge-Markovian is a relatively simple and comprehensive model of evolving graphs: every pair of…
Motivated by techniques developed in recent progress on lower bounds for sublinear time algorithms (Behnezhad, Roghani and Rubinstein, STOC 2023, FOCS 2023, and STOC 2024) we introduce and study a new class of randomized algorithmic…
Optimizing embedded systems, where the optimization of one depends on the state of another, is a formidable computational and algorithmic challenge, that is ubiquitous in real world systems. We study flow networks, where bilevel…
Efficient sampling of complex high-dimensional probability distributions is a central task in computational science. Machine learning methods like autoregressive neural networks, used with Markov chain Monte Carlo sampling, provide good…
A finite ergodic Markov chain is said to exhibit cutoff if its distance to stationarity remains close to 1 over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Discovered in the context of card…
Evolutionary algorithms (EAs) are universal solvers inspired by principles of natural evolution. In many applications, EAs produce astonishingly good solutions. As they are able to deal with complex optimisation problems, they show great…
We introduce discrete time Markov chains that preserve uniform measures on boxed plane partitions. Elementary Markov steps change the size of the box from (a x b x c) to ((a-1) x (b+1) x c) or ((a+1) x (b-1) x c). Algorithmic realization of…
In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…
We extend stochastic network optimization theory to treat networks with arbitrary sample paths for arrivals, channels, and mobility. The network can experience unexpected link or node failures, traffic bursts, and topology changes, and…
Scene graph generation is an important visual understanding task with a broad range of vision applications. Despite recent tremendous progress, it remains challenging due to the intrinsic long-tailed class distribution and large intra-class…
Detecting and visualizing what are the most relevant changes in an evolving network is an open challenge in several domains. We present a fast algorithm that filters subsets of the strongest nodes and edges representing an evolving weighted…
In modern data center networks, thousands of hosts contend for shared link capacity; the scale of these systems makes centralized scheduling impractical. This article models such scheduling as a bipartite matching problem under…
We propose a method for the classification of objects that are structured as random trees. Our aim is to model a distribution over the node label assignments in settings where the tree data structure is associated with node attributes…
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…
We consider a decentralized convex unconstrained optimization problem, where the cost function can be decomposed into a sum of strongly convex and smooth functions, associated with individual agents, interacting over a static or…
Establishing cutoff, an abrupt transition from "not mixed" to "well mixed", is a classical topic in the theory of mixing times for Markov chains. Interest has grown recently in determining not only the existence of cutoff and the order of…