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While the P vs NP problem is mainly approached form the point of view of discrete mathematics, this paper proposes reformulations into the field of abstract algebra, geometry, fourier analysis and of continuous global optimization - which…
Among various distance functions for graphs, graph and subgraph edit distances (GED and SED respectively) are two of the most popular and expressive measures. Unfortunately, exact computations for both are NP-hard. To overcome this…
This paper proposes a family of graph metrics for measuring distances between graphs of different sizes. The proposed metric family defines a general form of the graph generalised optimal sub-pattern assignment (GOSPA) metric and is also…
Similarity search is a fundamental task for exploiting information in various applications dealing with graph data, such as citation networks or knowledge graphs. While this task has been intensively approached from heuristics to graph…
As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…
We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of…
In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the…
We introduce new distance measures for comparing straight-line embedded graphs based on the Fr\'echet distance and the weak Fr\'echet distance. These graph distances are defined using continuous mappings and thus take the combinatorial…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…
General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…
Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More…
The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games…
This thesis studies the graph alignment problem, the noisy version of the graph isomorphism problem, which aims to find a matching between the nodes of two graphs which preserves most of the edges. Focusing on the planted version where the…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
Finding a simple path of even length between two designated vertices in a directed graph is a fundamental NP-complete problem known as the EvenPath problem. Nedev proved in 1999, that for directed planar graphs, the problem can be solved in…
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,…
We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence, where the aim is to obtain a graph with a given degree sequence \sigma by at most k vertex or edge deletions…
Understanding spatial correlation is vital in many fields including epidemiology and social science. Lee, Meeks and Pettersson (Stat. Comput. 2021) recently demonstrated that improved inference for areal unit count data can be achieved by…
We consider drawings of graphs in the plane in which vertices are assigned distinct points in the plane and edges are drawn as simple curves connecting the vertices and such that the edges intersect only at their common endpoints. There is…