Related papers: Synchronized Planarity with Applications to Constr…
A graph with n vertices is 1-planar if it can be drawn in the plane such that each edge is crossed at most once, and is optimal if it has the maximum of 4n-8 edges. We show that optimal 1-planar graphs can be recognized in linear time. Our…
We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization.…
Community-based graph clustering is one of the most popular topics in the analysis of complex social networks. This type of clustering involves grouping vertices that are considered to share more connections, whereas vertices in different…
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
A common approach for designing scalable algorithms for massive data sets is to distribute the computation across, say $k$, machines and process the data using limited communication between them. A particularly appealing framework here is…
We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…
We consider three simple quadratic time algorithms for the problem Level Planarity and give a level-planar instance that they either falsely report as negative or for which they output a drawing that is not level planar.
We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…
One way to define the Matching Cut problem is: Given a graph $G$, is there an edge-cut $M$ of $G$ such that $M$ is an independent set in the line graph of $G$? We propose the more general Conflict-Free Cut problem: Together with the graph…
This paper studies a scheduling problem in a parallel machine setting, where each machine must adhere to a predetermined fixed order for processing the jobs. Given $n$ jobs, each with processing times and deadlines, we aim to minimize the…
We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an…
We study two variants of \textsc{Maximum Cut}, which we call \textsc{Connected Maximum Cut} and \textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
Graph matching is one of the most important problems in graph theory and combinatorial optimization, with many applications in various domains. Although meta-heuristic algorithms have had good performance on many NP-Hard and NP-Complete…
We consider the following two algorithmic problems: given a graph $G$ and a subgraph $H\subseteq G$, decide whether $H$ is an isometric or a geodesically convex subgraph of $G$. It is relatively easy to see that the problems can be solved…
In this paper, we address the finite time synchronization of a network of dynamical systems with time-varying interactions modeled using temporal networks. We synchronize a few nodes initially using external control inputs. These nodes are…
We study the \emph{{interval completion}} problem, which asks for the insertion of a set of at most $k$ edges to make a graph of $n$ vertices into an interval graph. We focus on chordal graphs with no small obstructions, where every…
We consider the problem of grasping in clutter. While there have been motion planners developed to address this problem in recent years, these planners are mostly tailored for open-loop execution. Open-loop execution in this domain,…