Related papers: Minimum leader selection for Structural Controllab…
The minimum dominating set problem asks for a dominating set with minimum size. First, we determine some vertices contained in the minimum dominating set of a graph. By applying a particular scheme, we ensure that the resulting graph is…
Positive systems describing networks with inherently non-negative states and inputs arise naturally in routing, logistics, and compartmental modelling. We consider problems modelled as positive linear systems in incidence form with linear…
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…
This work proposes an extension to the leader-first follower (LFF) class of graphs used to solve the bearing-only formation control problem over directed graphs. The first contribution provides an equilibrium, stability, and convergence…
In the semi-supervised setting where labeled data are largely limited, it remains to be a big challenge for message passing based graph neural networks (GNNs) to learn feature representations for the nodes with the same class label that is…
We consider leader-follower multi-agent systems that have many leaders, defined on any connected weighted undirected graphs, and address the leader selection and demotion problems. The leader selection problem is formulated as a…
The power dominating set (PDS) problem is the following extension of the well-known dominating set problem: find a smallest-size set of nodes $S$ that power dominates all the nodes, where a node $v$ is power dominated if (1) $v$ is in $S$…
The Maximum Common Subgraph (MCS) problem plays a crucial role across various domains, bridging theoretical exploration and practical applications in fields like bioinformatics and social network analysis. Despite its wide applicability,…
Given an undirected graph $G = (V, E)$ and a weight function $w:E \to \mathbb{R}$, the \textsc{Minimum Dominating Tree} problem asks to find a minimum weight sub-tree of $G$, $T = (U, F)$, such that every $v \in V \setminus U$ is adjacent…
This paper studies output feedback consensus protocol design problems for linear multi-agent systems with directed graphs. We consider both leaderless and leader-follower consensus with a leader whose control input is nonzero and bounded.…
This paper considers the leader-follower tracking control problem for linear interconnected systems with undirected topology and linear dynamic coupling. Interactions between the systems are treated as linear dynamic uncertainty and are…
In this paper, we demonstrate a conflicting relationship between two crucial properties---controllability and robustness---in linear dynamical networks of diffusively coupled agents. In particular, for any given number of nodes $N$ and…
In the context of algorithm theory, various studies have been conducted on spanning trees with desirable properties. In this paper, we consider the \textsc{Minimum Cover Spanning Tree} problem (MCST for short). Given a graph $G$ and a…
Given a dominating set, how much smaller a dominating set can we find through elementary operations? Here, we proceed by iterative vertex addition and removal while maintaining the property that the set forms a dominating set of bounded…
Selecting a few available actuators to ensure the controllability of a linear system is a fundamental problem in control theory. Previous works either focus on optimal performance, simplifying the controllability issue, or make the system…
We are interested in assigning a pre-specified number of nodes as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. This problem arises in several applications including control of…
Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation…
We introduce a new bilevel version of the classic shortest path problem and completely characterize its computational complexity with respect to several problem variants. In our problem, the leader and the follower each control a subset of…
The Minimum Dominating Set (MDS) problem is one of the most fundamental and challenging problems in distributed computing. While it is well-known that minimum dominating sets cannot be approximated locally on general graphs, over the last…
Given a linear system, we consider the problem of finding a small set of variables to affect with an input so that the resulting system is controllable. We show that this problem is NP-hard; indeed, we show that even approximating the…