Related papers: Efficient k-step Weighted Reachability Query Proce…
Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in…
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…
We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…
Graph similarity search is a common and fundamental operation in graph databases. One of the most popular graph similarity measures is the Graph Edit Distance (GED) mainly because of its broad applicability and high interpretability.…
For an edge-weighted connected undirected graph, the minimum $k$-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into $k$ connected components. The problem is NP-hard when $k$ is part…
The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…
In the $2$-reachability problem we are given a directed graph $G$ and we wish to determine if there are two (edge or vertex) disjoint paths from $u$ to $v$, for a given pair of vertices $u$ and $v$. In this paper, we present an algorithm…
The graph isomorphism, subgraph isomorphism, and graph edit distance problems are combinatorial problems with many applications. Heuristic exact and approximate algorithms for each of these problems have been developed for different kinds…
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…
We present an interactive framework that, given a membership test for a graph class $\mathcal{G}$ and a number $k$, finds and tests unavoidable sets for the class of graphs in $\mathcal{G}$ of path-width at most $k$. We put special emphasis…
The problem of finding a path between two points while avoiding obstacles is critical in robotic path planning. We focus on the feasibility problem: determining whether such a path exists. We model the robot as a query-specific rectangular…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
The vertex PI index is a distance--based molecular structure descriptor, that recently found numerous chemical applications. In order to increase diversity of this topological index for bipartite graphs, we introduce weighted version…
The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields, from data mining to computational biology. Several variants of the problem have been considered,…
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…
We consider data-driven reachability analysis of discrete-time stochastic dynamical systems using conformal inference. We assume that we are not provided with a symbolic representation of the stochastic system, but instead have access to a…
Given a positive integer $k$, a $k$-dominating set in a graph $G$ is a set of vertices such that every vertex not in the set has at least $k$ neighbors in the set. A total $k$-dominating set, also known as a $k$-tuple total dominating set,…
Graph theory is increasingly commonly utilised in genetics, proteomics and neuroimaging. In such fields, the data of interest generally constitute weighted graphs. Analysis of such weighted graphs often require the integration of…
We study a class of reachability problems in weighted graphs with constraints on the accumulated weight of paths. The problems we study can equivalently be formulated in the model of vector addition systems with states (VASS). We consider a…
In a strongly connected graph $G = (V,E)$, a cut arc (also called strong bridge) is an arc $e \in E$ whose removal makes the graph no longer strongly connected. Equivalently, there exist $u,v \in V$, such that all $u$-$v$ walks contain $e$.…