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A recent research direction in data-driven modeling is the identification of dynamic networks, in which measured vertex signals are interconnected by dynamic edges represented by causal linear transfer functions. The major question…
We give an efficient algorithm that, given a graph $G$ and a partition $V_1,\ldots,V_m$ of its vertex set, finds either an independent transversal (an independent set $\{v_1,\ldots,v_m\}$ in $G$ such that $v_i\in V_i$ for each $i$), or a…
Data-driven approaches have been proven effective in solving combinatorial optimization problems over graphs such as the traveling salesman problems and the vehicle routing problem. The rationale behind such methods is that the input…
We consider the following problem arising from the study of human problem solving: Let $G$ be a vertex-weighted graph with marked "in" and "out" vertices. Suppose a random walker begins at the in-vertex, steps to neighbors of vertices with…
Increasing interest in integrating advanced robotics within manufacturing has spurred a renewed concentration in developing real-time scheduling solutions to coordinate human-robot collaboration in this environment. Traditionally, the…
We present a distributed anytime algorithm for performing MAP inference in graphical models. The problem is formulated as a linear programming relaxation over the edges of a graph. The resulting program has a constraint structure that…
We give a characterization of the effect of sequences of pivot operations on a graph by relating it to determinants of adjacency matrices. This allows us to deduce that two sequences of pivot operations are equivalent iff they contain the…
A dominating set in a graph is a set of vertices with the property that every vertex in the graph is either in the set or adjacent to something in the set. The domination sequence of the graph is the sequence whose $k$th term is the number…
The Transversal problem, i.e, the enumeration of all the minimal transversals of a hypergraph in output-polynomial time, i.e, in time polynomial in its size and the cumulated size of all its minimal transversals, is a fifty years old open…
Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the…
This paper proposes two novel distributed continuous-time algorithms inspired by PID control to solve distributed optimization problems. The algorithms are referred to as first-order and second-order, respectively, depend on the intrinsic…
In a simple connected graph $G=(V,E)$, a subset of vertices $S \subseteq V$ is a dominating set if any vertex $v \in V\setminus S$ is adjacent to some vertex $x$ from this subset. A number of real-life problems can be modeled using this…
We consider the following generalization of dominating sets: Let $G$ be a host graph and $P$ be a pattern graph $P$. A dominating $P$-pattern in $G$ is a subset $S$ of vertices in $G$ that (1) forms a dominating set in $G$ \emph{and} (2)…
Research involving computing with mobile agents is a fast-growing field, given the advancement of technology in automated systems, e.g., robots, drones, self-driving cars, etc. Therefore, it is pressing to focus on solving classical network…
The dual normal factor graph and the factor graph duality theorem have been considered for discrete graphical models. In this paper, we show an application of the factor graph duality theorem to continuous graphical models. Specifically, we…
Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, link prediction, and community detection. These models are usually designed to preserve the vertex information at…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…
We investigate the asymptotic number of induced subgraphs in power-law uniform random graphs. We show that these induced subgraphs appear typically on vertices with specific degrees, which are found by solving an optimization problem.…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
A hypergraph is a generalization of a graph where edges can connect any number of vertices. In this paper, we extend the study of locating-dominating sets to hypergraphs. Along with some basic results, sharp bounds for the…