Related papers: Shortest Paths in a Weighted Simplicial Complex
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
We study the sample complexity of estimating the covariance matrix $\mathbf{\Sigma} \in \mathbb{R}^{d\times d}$ of a distribution $\mathcal D$ over $\mathbb{R}^d$ given independent samples, under the assumption that $\mathbf{\Sigma}$ is…
Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among…
We present the first deterministic nearly-linear time algorithm for single-source shortest paths with negative edge weights on directed graphs: given a directed graph $G$ with $n$ vertices, $m$ edges whose weights are integer in…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
The aspect ratio of a (positively) weighted graph $G$ is the ratio of its maximum edge weight to its minimum edge weight. Aspect ratio commonly arises as a complexity measure in graph algorithms, especially related to the computation of…
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…
This paper proposes a new analysis of graph using the concept of electric potential, and also proposes a graph simplification method based on this analysis. Suppose that each node in the weighted-graph has its respective potential value.…
The shortest path problem is a typical problem in graph theory with wide potential applications. The state-of-the-art single-source shortest paths algorithm on the weight graph is the $\Delta$-stepping algorithm, which can efficiently…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in…
We show how to combine two techniques for efficiently computing shortest paths in directed planar graphs. The first is the linear-time shortest-path algorithm of Henzinger, Klein, Subramanian, and Rao [STOC'94]. The second is Fakcharoenphol…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Many exact search algorithms for NP-hard graph problems adopt the old Davis-Putman branch-and-reduce paradigm. The performance of these algorithms often suffers from the increasing number of graph modifications, such as vertex/edge…
We study the 2-Disjoint Shortest Paths (2-DSP) problem: given a directed weighted graph and two terminal pairs $(s_1,t_1)$ and $(s_2,t_2)$, decide whether there exist vertex-disjoint shortest paths between each pair. Building on recent…
We obtain the first near-linear time deterministic algorithm for negative-weight single-source shortest paths on integer-weighted graphs. Our main ingredient is a deterministic construction of a padded decomposition on directed graphs,…
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…
We introduce a method to reduce the study of the topology of a simplicial complex to that of a simpler one. We give some applications of this method to complexes arising from graphs. As a consequence, we answer some questions raised in…
Consider a finite directed graph without cycles in which the arrows are weighted. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context…