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A \emph{saddlepoint} of an $n \times n$ matrix is an entry that is the maximum of its row and the minimum of its column. Saddlepoints give the \emph{value} of a two-player zero-sum game, corresponding to its pure-strategy Nash equilibria;…
Given a set $S$ of $n$ line segments in the plane, we say that a region $\mathcal{R}\subseteq \mathbb{R}^2$ is a {\em stabber} for $S$ if $\mathcal{R}$ contains exactly one endpoint of each segment of $S$. In this paper we provide optimal…
A random walk (or a Wiener process), possibly with drift, is observed in a noisy or delayed fashion. The problem considered in this paper is to estimate the first time \tau the random walk reaches a given level. Specifically, the p-moment…
The determination of time-dependent collision-free shortest paths has received a fair amount of attention. Here, we study the problem of computing a time-dependent shortest path among growing discs which has been previously studied for the…
Object Permanence allows people to reason about the location of non-visible objects, by understanding that they continue to exist even when not perceived directly. Object Permanence is critical for building a model of the world, since…
Terrain Guarding Problem(TGP), which is known to be NP-complete, asks to find a smallest set of guard locations on a terrain $T$ such that every point on $T$ is visible by a guard. Here, we study this problem on 1.5D orthogonal terrains…
A common sensing problem is to use a set of stationary tracking locations to monitor a collection of moving devices: Given $n$ objects that need to be tracked, each following its own trajectory, and $m$ stationary traffic control stations,…
We establish limit theorems for the fluctuations of the rescaled occupation time of a $(d,\alpha,\beta)$-branching particle system. It consists of particles moving according to a symmetric $\alpha$-stable motion in $\mathbb{R}^d$. The…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
In this paper, we study the problem of moving $n$ sensors on a line to form a barrier coverage of a specified segment of the line such that the maximum moving distance of the sensors is minimized. Previously, it was an open question whether…
For two d-dimensional point sets A, B of size up to n, the Chamfer distance from A to B is defined as CH(A,B) = \sum_{a \in A} \min_{b \in B} \|a-b\|. The Chamfer distance is a widely used measure for quantifying dissimilarity between sets…
We show that for any set of $n$ points moving along "simple" trajectories (i.e., each coordinate is described with a polynomial of bounded degree) in $\Re^d$ and any parameter $2 \le k \le n$, one can select a fixed non-empty subset of the…
Being able to safely operate for extended periods of time in dynamic environments is a critical capability for autonomous systems. This generally involves the prediction and understanding of motion patterns of dynamic entities, such as…
A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More…
Nowadays large amounts of GPS trajectory data is being continuously collected by GPS-enabled devices such as vehicles navigation systems and mobile phones. GPS trajectory data is useful for applications such as traffic management, location…
We study the effect of a large obstacle on the so called residence time, i.e., the time that a particle performing a symmetric random walk in a rectangular (2D) domain needs to cross the strip. We observe a complex behavior, that is we find…
Imagine an island modeled as a simple polygon $\P$ with $n$ vertices whose coastline we wish to monitor. We consider the problem of building the minimum number of refueling stations along the boundary of $\P$ in such a way that a drone can…
We focus in this paper in the estimation of a target trajectory defined by whether a time constant parameter in a simple stochastic process or a random walk with binary observations. The binary observation comes from binary derivative…
Change-point detection and estimation procedures have been widely developed in the literature. However, commonly used approaches in change-point analysis have mainly been focusing on detecting change-points within an entire time series…
The wide spread use of positioning and photographing devices gives rise to a deluge of traffic trajectory data (e.g., vehicle passage records and taxi trajectory data), with each record having at least three attributes: object ID, location…