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Information diffusion in networks can be used to model many real-world phenomena, including rumor spreading on online social networks, epidemics in human beings, and malware on the Internet. Informally speaking, the source localization…
We study graph realization problems from a distributed perspective and we study it in the node capacitated clique (NCC) model of distributed computing, recently introduced for representing peer-to-peer networks. We focus on two central…
We study the problem of identifying the source of a diffusion spreading over a regular tree. When the degree of each node is at least three, we show that it is possible to construct confidence sets for the diffusion source with size…
The radius and diameter are fundamental graph parameters. They are defined as the minimum and maximum of the eccentricities in a graph, respectively, where the eccentricity of a vertex is the largest distance from the vertex to another…
We study a synchronous dispersion process in which $M$ particles are initially placed at a distinguished origin vertex of a graph $G$. At each time step, at each vertex $v$ occupied by more than one particle at the beginning of this step,…
We study the communication complexity of distributed offline dynamic programming, where a fixed batch dataset is partitioned across (M) machines connected by the data-induced dependency graph. We compare two paradigms: direct boundary-value…
Given a metric space $(X,d_X)$, a $(\beta,s,\Delta)$-sparse cover is a collection of clusters $\mathcal{C}\subseteq P(X)$ with diameter at most $\Delta$, such that for every point $x\in X$, the ball $B_X(x,\frac\Delta\beta)$ is fully…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
Suspensions of hard core spherical particles of diameter $D$ with inter-core connectivity range $\delta$ can be described in terms of random geometric graphs, where nodes represent the sphere centers and edges are assigned to any two…
Recent advances in robotic manipulation have highlighted the effectiveness of learning from demonstration. However, while end-to-end policies excel in expressivity and flexibility, they struggle both in generalizing to novel object…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
Understanding propagation structures in graph diffusion processes, such as epidemic spread or misinformation diffusion, is a fundamental yet challenging problem. While existing methods primarily focus on source localization, they cannot…
We study the distributed facility location games with candidate locations, where agents on a line are partitioned into groups. Both desirable and obnoxious facility location settings are discussed. In distributed location problems,…
We investigate the random close packing density, $\phi_\textrm{RCP}$, of polydisperse hard sphere systems using a theoretical framework based on the equilibrium model of crowding. We derive a closed-form solution for $\phi_\textrm{RCP}$ in…
The problem of how to estimate diffusion on a graph effectively is of importance both theoretically and practically. In this paper, we make use of two widely studied indices, geodesic distance and mean first-passage time ($MFPT$) for random…
Multi-Robot Coverage problems have been extensively studied in robotics, planning and multi-agent systems. In this work, we consider the coverage problem when there are constraints on the proximity (e.g., maximum distance between the…
It is a well known fact that sequential algorithms which exhibit a strong "local" nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number…
Local graph clustering and the closely related seed set expansion problem are primitives on graphs that are central to a wide range of analytic and learning tasks such as local clustering, community detection, nodes ranking and feature…
Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As…
We propose Distributed Neighbor Expansion (Distributed NE), a parallel and distributed graph partitioning method that can scale to trillion-edge graphs while providing high partitioning quality. Distributed NE is based on a new heuristic,…