Related papers: An efficient algorithm for $1$-dimensional (persis…
We present two algorithms for maintaining the topological order of a directed acyclic graph with n vertices, under an online edge insertion sequence of m edges. Efficient algorithms for online topological ordering have many applications,…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
In this paper tackle the problem of computing the ranks of certain eulerian magnitude homology groups of a graph G. First, we analyze the computational cost of our problem and prove that it is #W[1]-complete. Then we develop the first…
Classification of large and dense networks based on topology is very difficult due to the computational challenges of extracting meaningful topological features from real-world networks. In this paper we present a computationally tractable…
Link prediction (LP), inferring the connectivity between nodes, is a significant research area in graph data, where a link represents essential information on relationships between nodes. Although graph neural network (GNN)-based models…
Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In…
We study distributed computation in synchronous dynamic networks where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely)…
Persistent homology (PH) is a recently developed theory in the field of algebraic topology to study shapes of datasets. It is an effective data analysis tool that is robust to noise and has been widely applied. We demonstrate a general…
Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, and visual understanding. Generating such graphs enables tasks such as simulation, data…
We propose a new algorithm for numerical path tracking in polynomial homotopy continuation. The algorithm is `robust' in the sense that it is designed to prevent path jumping and in many cases, it can be used in (only) double precision…
In the age of real-time online traffic information and GPS-enabled devices, fastest-path computations between two points in a road network modeled as a directed graph, where each directed edge is weighted by a "travel time" value, are…
The approximate single-source shortest-path problem is as follows: given a graph with nonnegative edge weights and a designated source vertex $s$, return estimates of the distances from~$s$ to each other vertex such that the estimate falls…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian Completion Problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible…
Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
In the graph stream model of computation, an algorithm processes the edges of an input graph in one or more sequential passes while using a memory sublinear in the input size. This model poses significant challenges for constructing long…
In this work, we explore links between natural homology and persistent homology for the classification of directed spaces. The former is an algebraic invariant of directed spaces, a semantic model of concurrent programs. The latter was…