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The {\em bottleneck distance} is a natural measure of the distance between two finite point sets of equal cardinality, defined as the minimum over all bijections between the point sets of the maximum distance between any pair of points put…
We introduce a model of online algorithms subject to strict constraints on data retention. An online learning algorithm encounters a stream of data points, one per round, generated by some stationary process. Crucially, each data point can…
The ARRIVAL problem is to decide the fate of a train moving along the edges of a directed graph, according to a simple (deterministic) pseudorandom walk. The problem is in $NP \cap coNP$ but not known to be in $P$. The currently best…
Motivated by the problem of maintaining data structures for a large sets of points that are evolving over the course of time, we consider the problem of maintaining a set of labels assigned to the vertices of a tree, where the locations of…
Node connectivity plays a central role in temporal network analysis. We provide a comprehensive study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but edge sets changing over time. Taking into…
We study a family of reachability problems under waiting-time restrictions in temporal and vertex-colored temporal graphs. Given a temporal graph and a set of source vertices, we find the set of vertices that are reachable from a source via…
Computing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set is fixed but the edge set changes…
When analysing time series an important issue is to decide whether the time series is stationary or a random walk. Relaxing these notions, we consider the problem to decide in favor of the I(0)- or I(1)-property. Fixed-sample statistical…
To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…
We show that residence time measure can be used to identify the geometrical and transmission properties of a defect along a path. The model we study is based on a one--dimensional simple random walk. The sites of the lattice are regular,…
In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. In latent space random graphs, nodes are associated to unknown latent variables. One may then seek to compute distances directly in the…
Persistent monitoring missions require an up-to-date knowledge of the changing state of the underlying environment. UAVs can be gainfully employed to continually visit a set of targets representing tasks (and locations) in the environment…
Object permanence is the concept that objects do not suddenly disappear in the physical world. Humans understand this concept at young ages and know that another person is still there, even though it is temporarily occluded. Neural networks…
Several algorithms have been proposed for discovering patterns from trajectories of moving objects, but only a few have concentrated on outlier detection. Existing approaches, in general, discover spatial outliers, and do not provide any…
In a previous paper we showed that, for any $n \ge m+2$, most sets of $n$ points in $\RR^m$ are determined (up to rotations, reflections, translations and relabeling of the points) by the distribution of their pairwise distances. But there…
In this work, we tackle the problem of modeling the vehicle environment as dynamic occupancy grid map in complex urban scenarios using recurrent neural networks. Dynamic occupancy grid maps represent the scene in a bird's eye view, where…
Drones are becoming indispensable in many application domains. In data-driven missions, besides sensing, the drone must process the collected data at runtime to decide whether additional action must be taken on the spot, before moving to…
Consider a critical nearest neighbor branching random walk on the $d$-dimensional integer lattice initiated by a single particle at the origin. Let $G_{n}$ be the event that the branching random walk survives to generation $n$. We obtain…
In the \textsc{Waypoint Routing Problem} one is given an undirected capacitated and weighted graph $G$, a source-destination pair $s,t\in V(G)$ and a set $W\subseteq V(G)$, of \emph{waypoints}. The task is to find a walk which starts at the…
For any two point sets $A,B \subset \mathbb{R}^d$ of size up to $n$, the Chamfer distance from $A$ to $B$ is defined as $\text{CH}(A,B)=\sum_{a \in A} \min_{b \in B} d_X(a,b)$, where $d_X$ is the underlying distance measure (e.g., the…