Related papers: The graph alignment problem: fundamental limits an…
The densest $k$-subgraph problem is the problem of finding a $k$-vertex subgraph of a graph with the maximum number of edges. In order to solve large instances of the densest $k$-subgraph problem, we introduce two algorithms that are based…
Graph databases have been the subject of significant research and development. Problems such as modularity, centrality, alignment, and clustering have been formalized and solved in various application contexts. In this paper, we focus on…
Edge-labeled graphs are widely used to describe relationships between entities in a database. Given a query subgraph that represents an example of what the user is searching for, we study the problem of efficiently searching for similar…
In this paper, we consider the weighted graph matching problem with partially disclosed correspondences between a number of anchor nodes. Our construction exploits recently introduced node signatures based on graph Laplacians, namely the…
Graph alignment refers to the problem of finding a bijective mapping across vertices of two graphs such that, if two nodes are connected in the first graph, their images are connected in the second graph. This problem arises in many fields…
Machine learning and data mining algorithms have been increasingly used recently to support decision-making systems in many areas of high societal importance such as healthcare, education, or security. While being very efficient in their…
This paper deals with the problem of graph matching or network alignment for Erd\H{o}s--R\'enyi graphs, which can be viewed as a noisy average-case version of the graph isomorphism problem. Let $G$ and $G'$ be $G(n, p)$ Erd\H{o}s--R\'enyi…
We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their…
The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
Graph matching aims to find the latent vertex correspondence between two edge-correlated graphs and has found numerous applications across different fields. In this paper, we study a seeded graph matching problem, which assumes that a set…
Given a network, the critical node detection problem finds a subset of nodes whose removal disrupts the network connectivity. Since many real-world systems are naturally modeled as graphs, assessing the vulnerability of the network is…
The Graph Isomorphism problem has both theoretical and practical interest. In this paper we present an algorithm, called conauto-1.2, that efficiently tests whether two graphs are isomorphic, and finds an isomorphism if they are. This…
The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability…
This paper addresses the problem of matching $N$ weighted graphs referring to an identical object or category. More specifically, matching the common node correspondences among graphs. This multi-graph matching problem involves two…
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…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
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…
The stability method is very useful for obtaining exact solutions of many extremal graph problems. Its key step is to establish the stability property which, roughly speaking, states that any two almost optimal graphs of the same order $n$…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…