Related papers: Direct Paths in the Temporal Hypercube
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…
Consider a graph on $n$ uniform random points in the unit square, each pair being connected by an edge with probability $p$ if the inter-point distance is at most $r$. We show that as $n\to\infty$ the probability of full connectivity is…
Continuous 2-dimensional space is often discretized by considering a mesh of weighted cells. In this work we study how well a weighted mesh approximates the space, with respect to shortest paths. We consider a shortest path $…
An accessibility graph of a network contains a link, wherever there is a path of arbitrary length between two nodes. We generalize the concept of accessibility to temporal networks. Building an accessibility graph by consecutively adding…
We consider a directed variant of the negative-weight percolation model in a two-dimensional, periodic, square lattice. The problem exhibits edge weights which are taken from a distribution that allows for both positive and negative values.…
Random walks on expanders play a crucial role in Markov Chain Monte Carlo algorithms, derandomization, graph theory, and distributed computing. A desirable property is that they are rapidly mixing, which is equivalent to having a spectral…
In this work, we study a family of random geometric graphs on hyperbolic spaces. In this setting, N points are chosen randomly on a hyperbolic space and any two of them are joined by an edge with probability that depends on their hyperbolic…
A temporal random geometric graph is a random geometric graph in which all edges are endowed with a uniformly random time-stamp, representing the time of interaction between vertices. In such graphs, paths with increasing time stamps…
We introduce the algorithmic problem of finding a locally rainbow path of length $\ell$ connecting two distinguished vertices $s$ and $t$ in a vertex-colored directed graph. Herein, a path is locally rainbow if between any two visits of…
We consider random temporal graphs, a version of the classical Erd\H{o}s--R\'enyi random graph G(n,p) where additionally, each edge has a distinct random time stamp, and connectivity is constrained to sequences of edges with increasing time…
Let $X_1,..., X_n$ be independent, uniformly random points from $[0,1]^2$. We prove that if we add edges between these points one by one by order of increasing edge length then, with probability tending to 1 as the number of points $n$…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
In this paper we introduce a new network reachability problem where the goal is to find the most reliable path between two nodes in a network, represented as a directed acyclic graph. Individual edges within this network may fail according…
Temporal graphs are graphs where the edge set can change in each time step, and the vertex set stays the same. Exploration of temporal graphs whose snapshot in each time step is a connected graph, called connected temporal graphs, has been…
In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the standard theory for hypergraphs, this model is constructed from a bipartite graph. In our stochastic model,…
This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…
Topological spaces - such as classifying spaces, configuration spaces and spacetimes - often admit extra temporal structure. Qualitative invariants on such directed spaces often are more informative yet more difficult to calculate than…
Using Chen-Stein method in combination with size-biased couplings, we obtain the multivariate Poisson approximation in terms of the Wasserstein distance. As applications, we study the multivariate Poisson approximation of the distribution…
We consider a discrete-time TASEP, where each particle jumps according to Bernoulli random variables with particle-dependent and time-inhomogeneous parameters. We use the combinatorics of the Robinson-Schensted-Knuth correspondence and…
We present an exact formula for the ordinary generating series of the simple paths between any two vertices of a graph. Our formula involves the adjacency matrix of the connected induced subgraphs and remains valid on weighted and directed…