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We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…

This work concerns the analysis and design of distributed first-order optimization algorithms over time-varying graphs. The goal of such algorithms is to optimize a global function that is the average of local functions using only local…

Motivated by real-world applications such as the allocation of public housing, we examine the problem of assigning a group of agents to vertices (e.g., spatial locations) of a network so that the diversity level is maximized. Specifically,…

Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…

Several state-of-the-art neural graph embedding methods are based on short random walks (stochastic processes) because of their ease of computation, simplicity in capturing complex local graph properties, scalability, and interpretibility.…

In this paper, a novel approach is introduced which utilizes a Rapidly-exploring Random Graph to improve sampling-based autonomous exploration of unknown environments with unmanned ground vehicles compared to the current state of the art.…

Exploration is a fundamental problem in robotics. While sampling-based planners have shown high performance, they are oftentimes compute intensive and can exhibit high variance. To this end, we propose to directly learn the underlying…

MapReduce has become the de facto standard model for designing distributed algorithms to process big data on a cluster. There has been considerable research on designing efficient MapReduce algorithms for clustering, graph optimization, and…

The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…

Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…

Motion planning problems have been studied by both the robotics and the controls research communities for a long time, and many algorithms have been developed for their solution. Among them, incremental sampling-based motion planning…

We extend Random Access, a fundamental operation that enables efficient search and exploration algorithms, to the modern interactive data systems based on Ranked Retrieval and Similarity Search, where orderings are dynamically defined over…

We develop a new approach for approximating large independent sets when the input graph is a one-sided spectral expander - that is, the uniform random walk matrix of the graph has its second eigenvalue bounded away from 1. Consequently, we…

A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition [Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including Bayesian…

This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…

We identify the scaling limit of random intersection graphs inside their critical windows. The limit graphs vary according to the clustering regimes, and coincide with the continuum Erdos--Renyi graph in two out of the three regimes. Our…

We present a rectangle-based segmentation algorithm that sets up a graph and performs a graph cut to separate an object from the background. However, graph-based algorithms distribute the graph's nodes uniformly and equidistantly on the…

The dissertation is related to combinatorial geometry with a strong probabilistic flavor. The main results can be split into three parts. The results of the first part guarantee that each "unit distance graph" in the plane has an induced…

In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…

The problem of searching for a model-based scene interpretation is analyzed within a probabilistic framework. Object models are formulated as generative models for range data of the scene. A new statistical criterion, the truncated object…