Related papers: Beyond the shortest path: the path length index as…
We investigate the longest-path attacks on complex networks. Specifically, we remove approximately the longest simple path from a network iteratively until there are no paths left in the network. We propose two algorithms, the random…
Clustering trajectory data attracted considerable attention in the last few years. Most of prior work assumed that moving objects can move freely in an euclidean space and did not consider the eventual presence of an underlying road network…
Identifying influential spreaders in complex networks is a crucial problem which relates to wide applications. Many methods based on the global information such as $k$-shell and PageRank have been applied to rank spreaders. However, most of…
This work develops a generic framework, called the bag-of-paths (BoP), for link and network data analysis. The central idea is to assign a probability distribution on the set of all paths in a network. More precisely, a Gibbs-Boltzmann…
Addressing a quest by Gupta et al. [ICALP'14], we provide a first, comprehensive study of finding a short s-t path in the multistage graph model, referred to as the Multistage s-t Path problem. Herein, given a sequence of graphs over the…
In this article, we explicitly derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights. We determine the asymptotics of the degree distribution for large…
We consider the problem of finding a Hamiltonian path or a Hamiltonian cycle with precedence constraints in the form of a partial order on the vertex set. We show that the path problem is $\mathsf{NP}$-complete for graphs of pathwidth 4…
There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation…
Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely:…
Finding the shortest paths in road network is an important query in our life nowadays, and various index structures are constructed to speed up the query answering. However, these indexes can hardly work in real-life scenario because the…
We consider the NP-complete problem of tracking paths in a graph, first introduced by Banik et. al. [3]. Given an undirected graph with a source $s$ and a destination $t$, find the smallest subset of vertices whose intersection with any…
Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…
Evaluation of regular path queries (RPQs) is a central problem in graph databases. We investigate the corresponding enumeration problem, that is, given a graph and an RPQ, enumerate all paths in the graph that match the RPQ. We consider…
A geodesic is a shortest path which connects a pair of vertices of a graph G. In this paper we define the geodesic subpath number gpn(G) of a graph G as the number of geodesics in G. The number of subtrees and subpaths are already studied…
Let $G$ be a connected graph. The eccentricity of a path $P$, denoted by ecc$_G(P)$, is the maximum distance from $P$ to any vertex in $G$. In the \textsc{Central path} (CP) problem our aim is to find a path of minimum eccentricity. This…
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…
Computing shortest paths is a fundamental operation in processing graph data. In many real-world applications, discovering shortest paths between two vertices empowers us to make full use of the underlying structure to understand how…
For a graph $G$ and $p\in [0,1]$, let $G_p$ arise from $G$ by deleting every edge mutually independently with probability $1-p$. The random graph model $(K_n)_p$ is certainly the most investigated random graph model and also known as the…
We introduce and study the complexity of Path Packing. Given a graph $G$ and a list of paths, the task is to embed the paths edge-disjoint in $G$. This generalizes the well known Hamiltonian-Path problem. Since Hamiltonian Path is…
For the first time proposed: a method for representing the projections of a graph in computer memory and a description based on it of a quick search for shortest paths in unweighted dynamic graphs. The spatial complexity of the projection…