Related papers: Improved Approximation for Orienting Mixed Graphs
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…
We consider the following problem: Given an undirected (mixed) network and a set of ordered source-target, or cause-effect pairs, direct all edges so as to maximize the number of pairs that admit a directed source-target path. This is…
We aim to find orientations of mixed graphs optimizing the total reachability, a problem that has applications in causality and biology. For given a digraph $D$, we use $P(D)$ for the set of ordered pairs of distinct vertices in $V(D)$ and…
Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…
In the Upper Degree-Constrained Partial Orientation problem we are given an undirected graph $G=(V,E)$, together with two degree constraint functions $d^-,d^+ : V \to \mathbb{N}$. The goal is to orient as many edges as possible, in such a…
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
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…
The degree-diameter problem seeks to find the maximum possible order of a graph with a given (maximum) degree and diameter. It is known that graphs attaining the maximum possible value (the Moore bound) are extremely rare, but much activity…
A mixed graph $G$ is a graph that consists of both undirected and directed edges. An orientation of $G$ is formed by orienting all the undirected edges of $G$, i.e., converting each undirected edge $\{u,v\}$ into a directed edge that is…
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes…
Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…
When a large collection of objects (e.g., robots, sensors, etc.) has to be deployed in a given environment, it is often required to plan a coordinated motion of the objects from their initial position to a final configuration enjoying some…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
Given an undirected graph, one can assign directions to each of the edges of the graph, thus orienting the graph. To be as egalitarian as possible, one may wish to find an orientation such that no vertex is unfairly hit with too many arcs…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
In the classical facility location problem we consider a graph $G$ with fixed weights on the edges of $G$. The goal is then to find an optimal positioning for a set of facilities on the graph with respect to some objective function. We…
We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged.…
A mixed graph contains (undirected) edges as well as (directed) arcs, thus generalizing undirected and directed graphs. A proper coloring $c$ of a mixed graph $G$ assigns a positive integer to each vertex such that $c(u)\neq c(v)$ for every…
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…