Related papers: Polynomial-Time Algorithms for Structurally Observ…
It is $\mathsf{NP}$-hard to determine the minimum number of branching vertices needed in a single-source distance-preserving subgraph of an undirected graph. We show that this problem can be solved in polynomial time if the input graph is…
We consider minimal controllability problems (MCPs) on linear structural descriptor systems. We address two problems of determining the minimum number of input nodes such that a descriptor system is structurally controllable. We show that…
In this paper we investigate the controllability and observability properties of a family of linear dynamical systems, whose structure is induced by the Laplacian of a grid graph. This analysis is motivated by several applications in…
A monitoring edge-geodetic set of a graph is a subset $M$ of its vertices such that for every edge $e$ in the graph, deleting $e$ increases the distance between at least one pair of vertices in $M$. We study the following computational…
It is known that problems like Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal are polynomial time solvable in the class of chordal graphs. We consider these problems in a graph that has at most $k$ vertices whose deletion…
Brambles were introduced as the dual notion to treewidth, one of the most central concepts of the graph minor theory of Robertson and Seymour. Recently, Grohe and Marx showed that there are graphs G, in which every bramble of order larger…
We investigate graphs that can be represented as vertex intersections of horizontal and vertical paths in a grid, the so called $B_0$-VPG graphs. Recognizing this class is an NP-complete problem. Although, there exists a polynomial time…
It is known that determining the observability and reconstructibility of Boolean control networks (BCNs) are both NP-hard in the number of nodes of BCNs. In this paper, we use the aggregation method to overcome the challenging complexity…
In this paper, we show that given a weighted, directed planar graph $G$, and any $\epsilon >0$, there exists a polynomial time and $O(n^{\frac{1}{2}+\epsilon})$ space algorithm that computes the shortest path between two fixed vertices in…
In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…
We study partial and budgeted versions of the well studied connected dominating set problem. In the partial connected dominating set problem, we are given an undirected graph G = (V,E) and an integer n', and the goal is to find a minimum…
We present the first polynomial-time algorithm to exactly compute the number of labeled chordal graphs on $n$ vertices. Our algorithm solves a more general problem: given $n$ and $\omega$ as input, it computes the number of…
We study the problem of finding the smallest graph that does not occur as an induced subgraph of a given graph. This missing induced subgraph has at most logarithmic size and can be found by a brute-force search, in an $n$-vertex graph, in…
In this paper, we introduce a set representation called polynomial logical zonotopes for performing exact and computationally efficient reachability analysis on logical systems. We prove that through this polynomial-like construction, we…
In this paper, we study the structural state and input observability of continuous-time switched linear time-invariant systems and unknown inputs. First, we provide necessary and sufficient conditions for their structural state and input…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
Knots are commonly represented and manipulated via diagrams, which are decorated planar graphs. When such a knot diagram has low treewidth, parameterized graph algorithms can be leveraged to ensure the fast computation of many invariants…
In this paper, we study small-time local controllability of real analytic control-affine systems under small perturbations of their vector fields. Consider a real analytic control system $\mathcal{X}$ which is small-time locally…
An appropriate visualization of multiobjective non-dominated solutions is a valuable asset for decision making. Although there are methods for visualizing the solutions in the design space, they do not provide any information about their…
Motivated by the development and deployment of large-scale dynamical systems, often composed of geographically distributed smaller subsystems, we address the problem of verifying their controllability in a distributed manner. In this work…