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In the weighted load balancing problem, the input is an $n$-vertex bipartite graph between a set of clients and a set of servers, and each client comes with some nonnegative real weight. The output is an assignment that maps each client to…
The minimum completion (fill-in) problem is defined as follows: Given a graph family $\mathcal{F}$ (more generally, a property $\Pi$) and a graph $G$, the completion problem asks for the minimum number of non-edges needed to be added to $G$…
The Maximum s-Bundle Problem (MBP) addresses the task of identifying a maximum s-bundle in a given graph. A graph G=(V, E) is called an s-bundle if its vertex connectivity is at least |V|-s, where the vertex connectivity equals the minimum…
Let $W(G)$ be the Wiener index of a graph $G$. We say that a vertex $v \in V(G)$ is a \v{S}olt\'es vertex in $G$ if $W(G - v) = W(G)$, i.e. the Wiener index does not change if the vertex $v$ is removed. In 1991, \v{S}olt\'es posed the…
Stabilization of graphs has received substantial attention in recent years due to its connection to game theory. Stable graphs are exactly the graphs inducing a matching game with non-empty core. They are also the graphs that induce a…
Statistical inference on graphs is a burgeoning field in the applied and theoretical statistics communities, as well as throughout the wider world of science, engineering, business, etc. In many applications, we are faced with the reality…
We consider the minimization of edge-crossings in geometric drawings of graphs $G=(V, E)$, i.e., in drawings where each edge is depicted as a line segment. The respective decision problem is NP-hard [Bienstock, '91]. In contrast to theory…
Generally, a graph G, an independent set is a subset S of vertices in G such that no two vertices in S are adjacent (connected by an edge) and a vertex cover is a subset S of vertices such that each edge of G has at least one of its…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
The problem of increasing the centrality of a network node arises in many practical applications. In this paper, we study the optimization problem of maximizing the information centrality $I_v$ of a given node $v$ in a network with $n$…
We introduce the discrete-time treatment number of a graph, in which each vertex is in exactly one of three states at any given time-step: compromised, vulnerable, or treated. Our treatment number is distinct from other graph searching…
We consider the problem of covering a graph with a given number of induced subgraphs so that the maximum number of vertices in each subgraph is minimized. We prove NP-completeness of the problem, prove lower bounds, and give approximation…
This study considers the (soft) capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing…
We consider the problem of counting the number of vertices reachable from each vertex in a digraph $G$, which is equal to computing all the out-degrees of the transitive closure of $G$. The current (theoretically) fastest algorithms run in…
This paper presents a study on two data structures that have been used to model several problems in computer science: and/or graphs and x-y graphs. An and/or graph is an acyclic digraph containing a source, such that every vertex v has a…
In energy system analysis, coupling models with mismatched spatial resolutions is a significant challenge. A common solution is assigning weights to high-resolution geographic units for aggregation, but traditional models are limited by…
An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G and (ii) edge-weights on a complete undirected graph on the same vertex set. The objective is to find a subset of vertices satisfying some…
Given an ordering of the vertices of a graph, the cost of covering an edge is the smaller number of its two ends. The minimum sum vertex cover problem asks for an ordering that minimizes the total cost of covering all edges. We consider…
Motivated by the exact weight perfect matching problem and recent parameterized algorithms for finding an $\ell$-th smallest perfect matching, we study structural properties of edge-weight symmetries in graphs. Recent work by El Maalouly et…