Related papers: Angle Optimization of Graphs Embedded in the Plane
We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…
We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to…
The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a…
Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling…
Given a planar graph $G$ and a partition of the neighbors of each vertex $v$ in four sets $UR(v)$, $UL(v)$, $DL(v)$, and $DR(v)$, the problem Windrose Planarity asks to decide whether $G$ admits a windrose-planar drawing, that is, a planar…
Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often…
We discuss the design of interlayer edges in a multiplex network, under a limited budget, with the goal of improving its overall performance. We analyze the following three problems separately; first, we maximize the smallest nonzero…
We obtain an algorithmic meta-theorem for the following optimization problem. Let \phi\ be a Counting Monadic Second Order Logic (CMSO) formula and t be an integer. For a given graph G, the task is to maximize |X| subject to the following:…
We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…
A 1-plane graph is a graph embedded in the plane such that each edge is crossed at most once. A 1-plane graph is optimal if it has maximum edge density. A red-blue edge coloring of an optimal 1-plane graph $G$ partitions the edge set of $G$…
We study the Minimum Crossing Number problem: given an $n$-vertex graph $G$, the goal is to find a drawing of $G$ in the plane with minimum number of edge crossings. This is one of the central problems in topological graph theory, that has…
Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges…
Topological drawings are representations of graphs in the plane, where vertices are represented by points, and edges by simple curves connecting the points. A drawing is simple if two edges intersect at most in a single point, either at a…
A drawing in the plane ($\mathbb{R}^2$) of a graph $G=(V,E)$ equipped with a function $\gamma: V \rightarrow \mathbb{N}$ is \emph{$x$-bounded} if (i) $x(u) <x(v)$ whenever $\gamma(u)<\gamma(v)$ and (ii) $\gamma(u)\leq\gamma(w)\leq…
We consider the problem of augmenting an n-vertex graph embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present exact algorithms for the cases when (i) the input…
We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, including the (conditional) graph entropy, rate-distortion functions and…
We propose an approach to solve multi-agent path planning (MPP) problems for complex environments. Our method first designs a special pebble graph with a set of feasibility constraints, under which MPP problems have feasibility guarantee.…
We study the problem of finding the minimal (maximal) genus for a surface where a given four-valent graph with fixed opposite edge structure can be embedded into. We find several partial relations and give new reformulations in…
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…